IN  MEMORIAM 
FLOR1AN  CAJORI 


PRIMARY  ARITHMETIC 


BY 


DAVID   EUGENE    SMITH,  PH.D. 

\  ( 

PROFESSOR  OF  MATHEMATICS  IN  TEACHERS  COLLEGE 
COLUMBIA  UNIVERSITY,  NEW  YORK 


GINN   &  COMPANY 

BOSTON  •  NEW  YORK  •  CHICAGO  •  LONDON 


ENTERED  AT  STATIONERS'  HALL 


COPYRIGHT,  1904,  BY 
DAVID  EUGENE  SMITH 


ALL  RIGHTS  RESERVED 
25.3 


athenaeum 


GINN  &  COMPANY-  CAM- 
BRIDGE •  MASSACHUSETTS 


PEEFACE 

The   following    ideas    have  been    prominent  in   the 
preparation  of  this  book  : 

1.  In  sequence  of  topics,  to  follow  as  closely  as  pos- 
sible such  of  the  recent  courses  of  study  as  have  been  the 
most  carefully  prepared  for  our  public-school  systems. 
However  an  author  may  feel  as  to  details,  he  is  in  the 
main  bound  by  the  consensus  of  opinion  as  thus  expressed. 
The  purely  "  topical  method,"  the  attempt  to  exhaust  a 
subject  like   common  fractions   in  a  single  chapter,   is 
now  obsolete  in  our  leading  schools,  while  the  extreme 
"spiral  method"  is  scrappy,  uninteresting,  and  lacking 
in  the  continuity  so  essential  to  thoroughness.    Between 
these  two  comes  the  best  type  of  our  modern  courses  of 
study,  somewhat  spiral  in  arrangement,  in   that  most 
subjects  extend  over  several  terms,  but  admitting  of  a 
topical  arrangement  within  any  one  term,  thus  securing 
thoroughness  and  maintaining  an  interest. 

2.  In    arrangement    by    grades,    to    offer    merely   a 
tentative  plan  easily  modified  to  suit  local  conditions. 
Schools  cannot  all  be  graded  alike,  but  it  will  assist. 
teachers  to   kno\Y  that   the   successive   chapters   repre- 
sent the  average  work  of   the  first  four  school  years. 
Teachers  are  advised  to  introduce  the  book  at  the  mid- 


dle ofth^s^cond  j^ear,  reviewing-  the  first  chapter  and  a 
half  as  may  be  necessary. 

iii 


iv  PREFACE 

3.  In  the  selection  of  problems,  to  replace  the  arti- 
ficial ones,  against  which  teachers  have  so  long  pro- 
tested,   by  those    which   appeal   to    the    interests    and 
needs  of  children  in  the  primary  grades.     An  attempt 
has  also  been  made  so  to  group  these  problems  as  to 
emphasize  their  richness  of  content  in  relation  to  life. 
At  the  same  time   there  is   offered  an  abundance  of 
that  oral  and  written  drill  which  is  necessary  for  fixing 
number  facts  in  the  mind ;  the  former,  of  course,  being 
merely  suggestive  of  the  best  of  all  oral  work,   that 
which  appears  to  come  spontaneously  from  the  teacher. 
Supplementary  drill  work  will  be  found  on  page  266. 

4.  In  the  matter  of  method,  to  recognize  the  valu- 
able features  of  the  best  contributions,  avoiding  their 
extremes.     For  example,  there  should  always  be  some 
attention  to  a  spiral  arrangement,  but  its   extreme  is 
unscientific  and  uninteresting.     The  ratio  idea  in  frac- 
tions has  much  to  commend  it,  but  its  extreme  is  unnat- 
ural and  unbusinesslike.    The  actual  measuring  of  things 
is  valuable,  but  that,  like  paper  cutting  and  folding,  may 
be  carried  beyond  reasonable  bounds. 

5.  In   the    matter  of  illustrations,  to  recognize   the 
legitimate  use  of  pictures  for  the  following  purposes: 
To  show  the  relations  of  numbers,  to  make  real  their 
use  in  measurements,  to  suggest  materials  for  the  use 
of  the  teacher,  to  render  more  interesting  and  genuine 
the  various  groups  of  problems,  and  incidentally  to  pre- 
sent a  page  that  shall  attract  children  without  allowing 
the  book  to  become  a  mere  collection  of  pictures. 

DAVID  EUGENE  SMITH. 

February,  1904. 


TABLE  OF  CONTENTS 
CHAPTER  I 

REVIEW  OF  NUMBERS  TO  12 

PAGE 

COUNTING 1  . 

MEASURING  .......... 

ADDITION 6 

SUBTRACTION     .......... 

MULTIPLICATION 15 

PARTS  OF  ONE  OBJECT      ........  17 

PARTS  OF  A  GROUP  OF  OBJECTS .20 

FORMS 21 

MEASURES      .         .         .         .         .         .         *         .         .         .         .26 

LENGTH         ..........  26 

VALUE 28 

LIQUID  MEASURE 30 

WEIGHT 31 

CHAPTER  II 

I.  REVIEW  OF  NUMBERS  TO  100 

COUNTING  ...........  32 

BY  TENS .         .  .32 

To  ONE  HUNDRED        ........  34 

ADDITION       .         .         .         .         .         .         .         .         .         .  .35 

SUBTRACTION     ..........  41 

MULTIPLICATION    .         .         .         .         .         .         .         .         .  .45 

DIVISION   ...........  46 

NUMBER  TABLE 48 

TIME 49 

ROMAN  NUMERALS   .         .         .         .         .         .         .         .  .49 

THE  DOZEN 50 

II.   NUMBERS  TO  1000 

READING  AND  WRITING  NUMBERS         .         .         .         .         .         .61. 

MEASURES  ..........  55 

LENGTH 55 

WEIGHT  ..........  56 

CAPACITY 60 

ANGLES  .  .  .  .  .  •  .  .  .  .  62 

TIME 63 

SQUARE  MEASURE  .....  0  ..  64 


PRIMARY  ARITHMETIC 

CHAPTER  I 

REVIEW  OF  NUMBERS  TO  12 
COUNTING 

You  already  know  a  good  deal  about  numbers. 
You  learned  to  count  a  little  before  you  came  to 
school,  and  you  have  learned  much  more  since  that 
time.  Perhaps  every  one  in  your  class  can  count 
to  a  hundred.  How  far  can  you  count  ? 

You  know  about  buying  things  and  paying  for 
them,  and  perhaps  you  have  a  bank  with  some 
money  in  it. 

One  of  the  first  things  you  learned  about  num- 
bers was  counting.  You  learned  : 

Figures         0  123456 

Names       naught     one     two     three    four      five     six 

•  •  ••         •_•••• 


Figures         7            8             9  10  11           12 

Names      seven    eight       nine  ten  eleven  twelve 

n,.     •••   ••••  ••••  ••••  »•••  •••• 

Objects    •           •  ••  •••  •••• 

•••   ••••  •••• 

1 


PRIMARY   ARITHMETIC 


ORAL    EXERCISE 


1.  How  many  children  are  there  in  the  picture  ? 

2.  If  there  were   one   more,  how  many  would 
there  be  ? 

3.  If  there  were  three  less,  how  many  would 
there  be  ? 

4.  How  many  are  at  the  right  of   the   book  ? 
How  many  are  at  the  left  ? 

5.  How    many    more   are    seated   in  your   row 
to-day  than  in  the  picture  ? 

6.  Write    your   name   on   the    blackboard   and 
count  the  letters. 

7.  How   many   boys   are   there    in  your  class  ? 
How  many  girls? 

8.  How  many  words  are  there  in  this  line?  in 
the  first  line  of  Ex.  9  ? 

9.  Close  your  eyes  and  hear  me  tap  the  desk. 
How  many  taps  did  you  hear  ? 


COUNTING 


ORAL   EXERCISE 


1.  Close    your    eyes   and    tell   by   feeling   how 
many  pieces  of  crayon  I  have  in  my  hand. 

2.  If  you  call  the  front  desk  the  first,  and  the 
next  the  second,  and  so  on,  what  is  the  last  one  ? 

3.  How   many    days    make    a   week?      Sunday 
being  the  first,  what  is  the  number  of  this  day  ? 

4.  Copy  these  pictures  on    the  blackboard  and 
then  rapidly  tell,  without  counting,  the  number  of 
dots  in  each  group  : 


•  •        •     •         «  •••        •••  •  •     •  e 

5.  Copy  these  figures  on  the  blackboard  and 
read  them  rapidly: 

47936258 

The  teacher  should  daily  give  abundant  oral  drill  of  the  kind 
suggested  on  the  first  few  pages.  Let  there  be  no  day  without 
oral  drill,  using  objects  only  as  necessary.  Cards  prepared  by  the 
children,  showing  groups  as  in  Ex.  4,  are.  valuable  for  drill. 

j» 

WRITTEN  EXERCISE 

1.  Copy  these   pictures    and   write   the    figures 

below  them  : 

• 

•  •        ••         ••  •  oo  •  •         •    •       ••• 

•       •         •OS          000  O  •      •         •••          •      • 

•  900  ••  00  OO  00«  9  •      •          ••• 

• 

2.  Make   pictures   with  dots    or  lines   to  show 

5,  7,  6,  3,  9,  4. 


PRIMARY   ARITHMETIC 


ORAL   EXERCISE 

1.  What   measure  is   Will   using   to   find   how 

long    the    black- 
board is? 

2.  What  one  is 
Mary    using     to 
find  the  height  of 
the  blackboard? 

3.  How   many 
feet  long   is  the 
yardstick?  Meas- 
ure it  and  see. 

4.  Measure  the 
length    of     your 
own    blackboard 
in  feet;  in  yards. 

5.  How  many  feet  do  you  think  the  chalk  rack 
is  from  the  floor  ?     Measure  and  see. 

6.  How  many  inches  long  is  the  crayon  box  ? 
Measure  it  and  see. 

7.  How  much  longer  is  the  crayon  box  than  it 
is  wide  ? 

8.  Do  you  know  how  many  feet  tall  you  are? 
Measure  and  see.     This  is  how  much  more  than  a 
yard? 

9.  Draw  on  the  blackboard  a  line  that  you  think 
is  a  foot  long.    Then  measure  it  and  see  if  you  are 
right. 


MEASURING  5 

ORAL  EXERCISE 

1.  How  many  inches  wide  is  the  window  pane? 

2.  How  many  feet  long  is  your  desk,  and  how 
many  inches  over  ? 

3.  How  many  feet    and  inches  from   the   floor 
to  the  bottom  of  the  blackboard? 

4.  Stepping  as  you  usually  do  in  walking,  find 
how  many  paces  in  the  length  of  the  room. 

5.  How   many   paces   wide    do    you   think   the 
room  is  ?     Pace  the  width  and  see  if  you  are  right. 

6.  How  tall  do  you  think  you  are  ?     Measure. 
How  many  feet,  and  how  many  inches  over  ? 

7.  How  many  inches  from  the  lower  left-hand 
corner  of  this  page  to  the  upper  right-hand  corner  ? 

8.  How  wide  do  you  think  the  door  is  ?    Meas- 
ure.    How  many  feet,  and  how  many  inches  over? 

WRITTEN  EXERCISE 

1.  Draw  on  your  paper  a  picture  like  this,  only 
larger.  Write  in  the  squares  all  of  the  figures  from 
1  to  10. 


10 


2.  Draw  on  paper  a  line  3  inches  long.  Draw 
two  other  lines,  one  of  them  1  inch  longer  than 
the  first,  and  the  other  1  inch  shorter. ' 

What  interests  the  children  should  largely  determine  the 
nature  of  the  measurements  to  be  made  by  the  class. 


6  PRIMARY   ARITHMETIC 

ADDITION 
ORAL  EXERCISE 

1.  Count  to  twelve.     What  number  do  you  add 
each  time  ? 

2.  State  rapidly  these  sums  : 

123456789   10 
111111   111_1 

3.  Count  to  twelve  by  2's :  2,  4,  6,  and  so  on. 

4.  State  rapidly  these  sums  : 

123456789      10 

222222222_2 

The  sum  of  3  and  4  is  also  written  3  +  4  =  7.  The 
sign  +  means  and;  it  is  also  called  plus.  The  sign  = 
means  equals.  The  sum  of  3  and  4  is  7. 

The  teacher  will  find  sets  of  cards,  each  having  a  combination 
like  those  in  Exs.  2,  4,  useful  for  drill,  enlarging  the  set  as  the 
class  proceeds. 

But  little  written  work  should  be  given  at  first,  and  pupils 
should  be  required  to  do  this  quickly.  Loitering  brings  both 
inaccuracy  and  lack  of  interest. 

WRITTEN  EXERCISE 

Copy  the  following    and   torite  the  sum,   thus: 

3  +  5-8. 

1.  2-1-1.     2.  2  +  3.     3.  2  +  5.     4.  7  +  2.       5.  6  +  1. 
6.  3  +  2.     7.  2  +  5.     8.  3  +  3.     9.  4  +  1.     10.  4  +  2, 


ADDITION  7 

ORAL  EXERCISE 
SOME  OF  YOUR  PURCHASES 

1.  How  much  do  two  2-cent  stamps  cost? 

2.  How  much  do  three  2-cent  stamps  cost  ? 

3.  Alice  paid  4  cents  for  a  pencil  and  5  cents 
for  a  pad  of  paper.     How  much  did  both  cost  ? 

You  have  now  found  that 
2  =  1  +  1 
3-1  +  2-24-1 
4-1+3-2+2-3+1 

5-1  +  4-2  +  3-3  +  2-4  +  1 
6-1+5-2+4-3+3-4+2-5+1 
7=1+6-2+5-3+4-4+3-5+2-6+1 
8-1+7-2+6-3+5-4+4-5+3-6+2 

-7  +  1 
9-1+8-2+7-3+6=4+5-5+4-6+3 

=7+2-8+1 
10-1+9-2+8-3+7-4+6-5+5=6+4 

=  7  +  3-8  +  2-9  +  1. 

A  little  rapid  oral  drill  on  this  table  and  the  subtraction  table 
on  page  14  should  form  part  of  the  daily  exercise  of  the  class. 
Cards  are  helpful,  as  suggested  on  page  6. 

WRITTEN  EXERCISE 

Make  pictures  like   this,    showing    the 
following  sums.      Write  the  answers. 

1.  2  +  5.    2.  6  +  0.    3.  4  +  2.    4.  3  +  5. 


PRIMARY   ARITHMETIC 


ORAL  EXERCISE 

1.  If  you  had  6  marbles,  and  I  gave  you  2  more, 
and  you  found  another,  how  many  would  you  have  ? 

2.  Rob's  pets  are  2  rabbits,  a  dog,  and  2  cats. 
How  many  pets  has  he  ? 

3.  See  how  rapidly  you  can  tell  the  sums  of  +he 

inner  and  outer  num- 
bers. State  only  the 
sums. 

These  figures  should  be 
placed  on  the  board  by  the 
teacher. 

4.  Tell  these  sums 
•)3  as  quickly  as  you  can, 
going    around   each 
wheel  both  ways. 
5.  If  Clara's  dog  Jack  was  2  months  old  when 
she  bought  him,  and  she  has  had  him  8  months, 
how  old  is  he  now  ? 


Accustom  the  pupils  to  read  combinations  as  they  read  words. 
When  they  see  the  word  one  they  do  not  stop  to  spell  it,  o,  n,  e. 
They  look  at  it  and  say  "  one."  So  when  they  see  this 
column  of  figures  they  should  say  « eight,"  not  stopping 
to  say  "  3  and  5  are  8." 


5 
3 


6.  State  the  sums  at  once  without  naming  the 
numbers  added : 

465522324235 
444536781861 


ADDITION  9 

ORAL   EXERCISE 

1.  State  rapidly  these  sums  : 

23456789 
33333333 

2.  State    rapidly   these    sums,    giving  only  the 
answers  without  naming  the  numbers : 

45678 
44444 

3.  I  am  thinking  of  two  numbers  whose  sum  is 
7  ;  they  are  not  6  and  1 ;  what  may  they  be  ? 

4.  Write  these  numbers  on  the  blackboard  and 
tell  the  sums  as  I  point  to  the  numbers : 

1         3        2         7        6         3   v     5         9 
42522331 

5.  Show  a  part  of  the  ruler  that  is   3  inches 
long.    Add  an  inch.     Now  how  long  is  the  part? 
Point  to  the  sum  of  3  inches  and  2  inches. 

WRITTEN  EXERCISE 

Measure  and  write  the  following  lengths  in  indies : 

1.  Length  of  your  pencil. 

2.  Width  and  length  of  your  paper. 

3.  Width  and  length  of  your  reading  book. 

Work  in  making  paper  boxes  and  envelopes,  from  measurement, 
is  also  valuable,  furnishing  to  children  an  interesting  motive. 


10  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  In  these    examples  in  addition,  look  at  one 
set  at  a  time,  close  your  eyes  and  tell  the  missing 
number : 

52*35*54* 
2*74*63*5 
*69*89*59 

2.  Look  carefully  at  these  numbers,  one  set  at 
a  time.     Then  close  your  eyes  and  think  of  them, 
telling  each  time  the  missing  number : 


3.  State  the  results  of  the  following : 

5786521 

+2     +1     +1     +3     +3     +6     +  7 

4.  If  Mary  has  3  cents,  and  Helen  has  4  cents, 
and  Bessie  has   2    cents,   how   much   have   they 
together  ? 

To  put  one  number  with  another  is  called  addition. 
The  result  is  called  the  sum. 

WRITTEN   EXERCISE 

Copy  the  following  and  write  the  sums: 

1.  4  +  3,  2  +  5,  6  +  1,  3  +  4. 

2.  6  +  2,  5  +  3,  1  +  7,          4  +  4. 

3.  3  +  3,  5  +  1,  2  +  4,          1  +  G. 


SUBTRACTION  11 

SUBTEACTION 

ORAL  EXERCISE 

1.  How  many  blocks  has  Helen  taken  from  the 
7  blocks  ? 

2.  After    tak- 
ing these  away, 
how  many  blocks 
are  left  ? 

3.  If  from  the 
7  blocks  she  took 
away  4   blocks, 

how  many  would  be  left  ? 

4.  How  many  are   4   blocks  and  3  blocks  ?   3 
blocks  and  4  blocks? 

5.  How   many   are  7  blocks  less   2  blocks  ?    7 
blocks  less  5  blocks  ? 

6.  How  many   are    6   blocks  and    1    block  ?    1 
block  and  6  blocks  ? 

7.  How  many  are  3  blocks  and  2  blocks  ?     How 
many  more  will  make  7  ? 

We  read  7  —  3,  "  seven  less  three,"  or  "  seven  minus 
three."  To  take  one  number  from  another  is  called 
subtraction.  The  result  is  called  the  difference. 

8.  How  many  more  blocks  would  Helen  need,  to 
have  9?    10? 

9.  How  many  blocks  should  she  take  from  the 
7  blocks  to  have  2  left  ? 


12  PRIMARY    ARITHMETIC 

ORAL  EXERCISE 

1.  How  many   are    6  marbles  less    4  marbles? 
4  marbles  and  2  marbles  ? 

2.  How  many  are  8  inches  less  5    inches?     5 
inches  and  3  inches  ?     3  inches  and  5  inches  ? 

3.  How  many  are  9  children  less  4  children? 
9    children   less    5   children?     5    children    and   4 
children  ? 

4.  Close  your  eyes  and  think  of  6  +  3  =  9.     Then 
think  of  6  +  *  =  9,  and  tell  the  missing  number. 

5.  Close  your  eyes  and  think  of  these      .        . 
numbers.     Then  think  of  them,  and  tell 

the  missing  number. 

6.  State  the  results  of  the  following : 

7899888 


The  teacher  should  give  abundant  oral  work  of  this  kind, 
leading  the  children  to  visualize  the  numbers  as  groups  and 
their  representation  by  figures. 

As  may  be  necessary  in  this  review,  the  teacher  may  use  splints, 
blocks,  or  number  cards  or  drawings  of  this  nature  : 


••  —  • 

•  •       •  • 

4  +  3=7  "  7       -4  =  3 

If  you  buy  a  3-cent  pencil  and  give  the  dealer  5 
cents,  he  says  to  himself  "  3  and  2  are  5,"  and  he  gives 
you  2  cents  in  change.  He  subtracts  3  from  5  by 
thinking  of  adding  2  and  3,  because  this  is  easier. 


SUBTRACTION 


13 


ORAL  EXERCISE 

1.  Jennie  is  buying  apples  from  Kate  at  1  cent 
each.     If  she  buys  2  apples,  and  gives  Kate  10 
cents,  how  much  change  should  she  get? 

2.  If  she  buys  5  cents'  worth  of  candy,  how  much 
change    should 

she  get  if  she 
pays  Kate  10 
cents  ? 

3.  How  much 
money    should 
she   pay   Kate 
for  2   popcorn 
balls  at  2  cents 
each?     What 

change  should  she  get  if  she  gives  Kate  a  5-cent 
piece  ? 

4.  If  Jennie  buys  2  apples  at  1  cent  each,  and 
5   cents'  worth  of  candy,  and  4   cents'  worth  of 
popcorn  balls,  how  much  will  she  pay  for  all? 

5.  Kate    sells    lemonade    at    3    cents    a    glass. 
Jennie   gives    her   5    cents.     How   much   change 
should  she  get? 


WRITTEN  EXERCISE 

Copy  the  following  and  write  the  answers : 

686734 
-4       -5       -2       -1       -1 


5 
3 


14  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  How  much  change  should  you  get  if  you  buy 

a  4-cent  pencil  and 
give  the  merchant 
1 6  5  cents? 

2.  See  how  rap- 
idly you  can  tell  the 
differences  of  the  inner  and  outer  numbers.  State 
only  the  differences. 

3.  State  rapidly  the  following  differences: 


10 

10 

10 

10 

10         10         10         10         10 

1 

2 

_3 

4 

5         _6           7           8           9 

9 

9 

9 

9 

9999 

1 

2 

3 

4 

5678 

8 

8 

8 

8 

888 

1 

2 

3 

4 

567 

7 

7 

7 

7 

7           7 

1 

2 

3 

4 

5          6 

6 

6 

6 

6 

6 

1 

2 

3 

4 

5         The  circles  in  Ex.  2  should 

— 

~~ 

"~ 

~~ 

be  placed  on  the  blackboard. 

5 

5 

5 

5 

Ex.  1  furnishes  a  valuable  type 

1 

2 

3 

4 

for  drill  work. 

This  table  of  differences  must 

4. 

4 

-j 

o 

Q 

be  memorized.    Change  the  regu- 

JL 

& 

*j 

lar  order  of  numbers  in  reviews. 

3 

3 

In  general  the  teacher  should 

1 

2 

drill  on  column  work  chiefly,  this 

being  the  form  which  pupils  need 

2 

to   visualize,    but  the   circle  drill 

1 

furnishes  a  variety. 

MULTIPLICATION  15 

MULTIPLICATION 


ORAL  EXERCISE 

1.  How  many  cubes   are   there  in  2 
each  pile  ?  22 

2.  Count  them  rapidly  by  2's,  thus:  222 
2,  4,  6,  and  so  on.  2222 

3.  Tell  the  number  of  2's  in  each  ?  ?    2    2    2 
of  these  columns,  and  the  sum.  3 

4.  Count  rapidly  by  3's  from  3  to  33 
12.     Tell  the  number  of  3's  in  each  333 
of  these  columns,  and  the  sum. 

5.  Here  are  two  4's,  and  also    9     9  0     o  =  4 
four  2's.    What  does  this  tell  you    *     *  0     9  _  4 
about  2  times  4  and  4  times  2?        2  + 


The  object  at  this  time  is  merely  to  give  an  idea  of  multipli- 
cation as  growing  out  of  addition. 

WRITTEN  EXERCISE 

Copy  the  following  and  write  the  answers: 

1.  2  +  2  +  2,  3  +  3, 

3  times  2,  2  times  3. 

2.  2  +  2  +  2  +  2,       .          4  +  4, 

4  times  2,  2  times  4. 


16  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 
SOME  OF  YOUR  PURCHASES 

1.  How  much  will  three  2-cent  stamps  cost  ? 

2.  At  5  cents   each,  how  much  will  2   oranges 
cost? 

3.  At  3  cents  a  pint,  how  much  will  3  pints  of 
milk  cost  ? 

4.  At  2  cents  a  yard,  how  much  will  4  yards  of 
ribbon  for  some  badges  cost  ? 

5.  A  nickel  is  5    cents.     How  many  cents  are 
there  in  2  nickels  ? 

6.  A  dime  is  10  cents.     This  is  how  many  times 
5  cents  ?     Then  a  dime  equals  how  many  nickels  ? 

We  may  write  2  times  3  cents  either  2x3  cents  or 
8  cents  x  2. 

Some  teachers  use  one,  some  the  other.  In  this  book  the 
work  in  general  allows  for  either  reading.  To  avoid  confusing 
children,  one  form  should  be  adopted  and  followed.  The  second 
form  is  preferably  read,  "  3  cents  multiplied  by  2." 

WRITTEN   EXERCISE 

1.  Copy  and  multiply: 

1x2          2x2  3x2          4x1 

2.  Draw  a  picture  of  a  square  1  inch  on  a  side. 
This  is  a  square  inch. 

3.  Draw   a  picture  of  a  square  2  inches  on   a 
side.     Divide  it  into  square  inches.     How  many 
square  inches  does  it  contain  ? 


FRACTIONS  17 

PARTS   OF   ONE   OBJECT 

ORAL  EXERCISE 

1.  Into  how  many  equal  parts  has  this  sphere 
been  divided  ?    Each  is  what  part  of  the  sphere  ? 

2.  If   the    sphere   weighs 
1    pound,    how   much    does 
half  of  it   weigh? 

3.  How  much  is  half  of 

the  sphere  and  half  of  the  sphere  ?     How  much  is 
half  of  a  foot  and  half  of  a  foot  ? 

One  half  is  written  l. 
We  write  two  halves  f . 

If  we  cover  a  half  sphere  in  the  picture,  we  leave 
a  sphere  and  a  half.  One  and  one  half  is  written  1^. 

No  abstract  seat  work  in  number  should  be  given  until  the 
pupil  can  do  it  without  mistake.  Premature  work  of  this  kind 
results  in  'habits  of  inaccuracy.  All  written  work  should,  there- 
fore, be  modified  as  necessary  for  individual  cases.  Teachers 
should  give  abundant  practice  on  halves,  using  drawings,  paper 
folding  and  cutting,  and  other  objective  work. 

WRITTEN  EXERCISE 

1.  Write  in  figures :  two  and  a  half. 

2.  Copy  and  add: 

i  +  i          H  +  J          i  +  i 

3.  Write    in    figures,    with    the    answers:    Two 
halves   are   how   many  ?      Four   halves   are   how 
many? 


18  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  What  part  of  the  sphere  is  C  ? 

2.  B  is  how  many  times  as  large  as  C  ? 

3.  If  you  write  one 
half  ^,  how  should  you 
write  one  fourth  ?  one 
third  ? 

4.  If  you   put    two 
fourths  of  a  sphere  together,  what  part  will  you 
have? 

5.  Add  J  of  a  sphere  and  -£  of  a  sphere;  ^  of 
a  sphere,  ^  of  a  sphere,  and  |  of  a  sphere. 

6.  Subtract  |  of  a  sphere  from  ^  of  a  sphere. 

The  above  is  suggestive  of  a  large  amount  of  rapid  oral  drill 
with  various  objects.  Paper  cutting  or  folding  may  be  employed 
to  advantage  in  this  connection.  For  example,  strips  of  paper 
may  be  cut  by  the  children  into  1-foot  lengths,  folded  to  get  the 
J-foot,  and  again  to  get  the  J-foot,  the  number  of  inches  being 
found  by  measuring. 

You  have  now  seen  that 

1.+  \  =  %,  and  that  f  =  1; 

i  +  t  =  !»  and  that  1  =  J- 
One  fourth  is  also  called  a  quarter. 

WRITTEN  EXERCISE 

1.  Draw  a  line  4  inches  long  and  divide  it  into 
fourths. 

2.  Draw  another  line  the  same  length,  making 
A  of  it  heavier  than  the  rest. 


FRACTIONS  19 


ORAL  EXERCISE 

1.  Block  B  is  how  many  times  as  large  as  C  ? 
Then  C  equals  what  part  of  B  ? 

2.  Block  A  is  how  many  times  as  large  as  C  ? 
Then  C  equals  what  part  of  A  ? 

3.  If  C  weighs  1  pound,  how  much  does  B  weigh? 
If  B  weighs  1  pound,  how  much  does  C  weigh? 

4.  If  C  weighs  1  pound,  how  much  do  A  and  B 
together  weigh  ? 

5.  If  B  weighs  1  pound,  how  much  do  A  and  C 
together  weigh? 

6.  If  C  is  1  foot  high,  how  high  is  A?     If  B  is 
1  foot  high,  how  high  is  C  ? 

7.  Is  C   more  or   less  than  half  of  A?     Then 
which  is  greater,  ^  or  \  ? 

WRITTEN  EXERCISE 

Copy  and  complete  the  following : 

1-      +     +     =  *-        2.       -     =  *•       3.    l-i  =  *. 


20  PRIMARY   ARITHMETIC 


PAKTS  OF  A  GROUP  OF  OBJECTS 

ORAL  EXERCISE 

1.  Here   are   6   little    rabbits   and   the    mother 
rabbit.     How  many  little  rabbits  on  each  side  ? 

2.  Half   of  6    rabbits   are  how  many  rabbits  ? 
How  many  pairs  are  half  of  6  pairs  of  ears  ?    How 
many  sets  are  half  of  6  sets  of  feet  ? 

3.  If  you  separate   the    six   little    rabbits  into 
3  equal  groups  instead  of  2   groups,  how  many 
will  there  be  in  each  group  ? 

4.  Then  how  many  are  |  of  6  rabbits  ?   ^  of  6 
ears  to  the  right  of  the  mother  rabbit  ?   ^  of   6 
bright  eyes  to  the  left  of  the  mother  rabbit? 

5.  How  many  is 

i  of  4  ?  J  of  6  ?  i  of  8  ?  i  of  10  ?  |  of  6  ?  1  of  9  ? 


We  find  ^  of  a  number  by  dividing  it  into  2  equal 
parts.  So  we  find  ±  of  6  blocks  by  dividing  them  into  2 
equal  groups.  We  write  this,  6  blocks  -s-  2  =  3  blocks, 

6.  How  many  are  10  blocks  -*•  2  ?   8  cents  -*-  2  ? 


LINES 


21 


FORMS 

ORAL    EXERCISE 

1.  This  little    girl   is   pointing   to  the  horizon. 
What  lines    in  the 

picture  are  nearly 
horizontal  ?  Why 
are  they  called  hor- 
izontal ? 

2.  Point   to   two 
nearly  vertical  lines 
in  the  picture. 

3.  If  you  hang  an 
apple  by  a  string, 
which  of  these  two 
kinds  of  lines  will 
the  string  show? 

4.  Point    to    six 
vertical  lines  in  the  room; 
to  ^  as  many  horizontal  lines. 


A  Horizontal  Line 


WRITTEN    EXERCISE 

1.  Draw  8  vertical  lines.     Cross  oft  \ 
of  them. 

2.  Draw  6  horizontal  lines,   making  | 
of  them  half  as  long  as  the  rest. 

3.  Draw  vertical  lines  as  in  Ex.  5  on 
page  20?  to  show  ^  of  8. 


o 

A  Vertical 
Line 


22  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  Point  to  a  right  angle  in  the  room ;  on  your 
desk. 

2.  Draw    on    the    blackboard    a   vertical   line. 
Draw  a  horizontal  line  that  meets  it.     What  kind 
of  an  angle  is  made? 

3.  Draw  an  oblong   on   the   blackboard.     How 
many  angles  are  there  in  the  oblong  ?     What  kind 
of  an  angle  is  each  one? 

4.  Draw    a   square   on   the   blackboard.      How 
many  sides  has  the  square?      How  many  right 
angles  ?     What  can  you  tell  about  the  sides  ? 

PAPER  FOLDING 

Schools  that  introduce  paper  folding  or  cutting  will  find  this 
subject  of  value  at  this  time. 

1.  Fold  or  cut  an  oblong  that  is  half  as  high  as 
it  is  long. 

2.  Fold  or  cut  one  that  is  three  times  as  long  as 
it  is  high. 

3.  Fold  or  cut  one  that  is  2  inches  long  and  | 
as  high. 

4.  Fold  one  that  is  4  inches  high  and  ^  as  long. 

5.  Fold  a  square  2  inches  on  a  side.     Divide  this 
into  four  squares  by  two  folds  of  the  paper. 

6.  Fold  or  cut  an  oblong  4  inches  long  and  3 
inches  high.     Fold  so  as  to  divide  this  into  small 
squares  1  inch  on  a  side. 


OBLONGS  23 

ORAL  EXERCISE 

1.  Point   to   %   of   these   squares.     How   many 
squares  are  %  of  8  squares  ? 

2.  Show  that  J  of  the  oblong 
equals  2  fourths,  and  that  4  fourths 
of  the  oblong  is  the  whole. 

3.  How  many  are   ^  of  8    squares?     Point  to 
them  in  two  different  groups.     How  many  halves 
make  the  whole  ? 

The  distance  around  a  figure  like  a  square  or  oblong 
is  called  the  perimeter. 

4.  Each  small  square  in  the  picture  is  ^  inch  on 
a  side.     How  long  is  the  perimeter  of  the  oblong  ? 

WRITTEN  EXERCISE 

1.  Draw  a  square  2  inches  on  a  side.     Divide  it 
into  squares  each  1  inch  on  a  side.     Each  small 
square  is  what  part  of  the  large  one  ? 

2.  Draw  an   oblong  1  inch  high  and  3  inches 
long.    Divide  it  into  squares  each  1  inch  on  a  side. 
Each  square  is  what  part  of  the  oblong  ? 

3.  If  a  square  is  2  inches  on  a  side,  how  long  is 
the  perimeter  ?    Draw  the  square  and  divide  it  into 
squares  each  ^  inch  on  a  side. 

4.  Draw   a    square    that   is    1    inch   high,    and 
another  that  is  2  inches  high.     The  second  equals 
how  many  times  the  first  ?     The  first  equals  what 
part  of  the  second  ? 


24  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

I.  If  this  prism  is  4  inches  high  and  is  ^   as 

thick,  how  thick  is  it  ? 

2.  If  it  weighs  3  pounds,  how  much 
would  it  weigh  if  it  were  only  ^  as  high? 

3.  If  it  weighs  3  pounds,  how  much 
would  it  weigh  if  it  were  twice  as  high? 

4.  The  ends  of  these  prisms  are  1  inch  square ; 

A  is  1  inch  long  and  B  is  4  inches 
long.     If  we  call  A  one.,  what  is  B  ? 
If  we  call  B  one,  what  is  A  ?     If  we 
call  A  two,  what  is  B  ? 

5.  If  we  call  cylinder  A  one,  what  is 
cylinderB?    what  is  C  ? 

6.  If  we  call  cylinder  B 
one,  what   is 

cylinder     A  ? 
what  is  C? 

7.  If  we  call  cylinder  B  two,  what  is  A?   what 
isC? 

8.  If  we  call  cylinder  C  one,  what  is  B  ?   what 
is  A? 

9.  If  B  weighs  1  pound,  how  much  does  A  weigh  ? 
how  much  does  C  weigh? 

10.  If  C  weighs  1  pound,  how  much  does  B  weigh  ? 
how  much  does  A  weigh  ? 

II.  If  B  is  4  inches  high,  how  high  is  A?   how 
high  is  C? 


SPHERES  25 


ORAL   EXERCISE 

1.  A  is  a  sphere.    C  is  what  part  of  a  sphere  ? 

2.  If  D  is  J  as  large  as  C,  what  part  of  a  sphere 
isD? 

3.  If  we-  call  A  four,  what  is  C  ? 

4.  If  we  call  A  eight,  what  is  C  ?  what  is  D  ? 

5.  Point  to  %  of  a  sphere ;  to  |  of  a  sphere ;  to 
three  times  \  of  a  sphere. 

The  above  may  easily  be  varied  by  using  parts  of  any  object. 
Paper  cutting  and  folding  are  recommended  for  this  work. 
Enough  such  oral  work  should  be  given  to  make  the  pupil 
entirely  familiar  with  these  fractions.  Incidentally  other  frac- 
tions may  be  introduced. 

WRITTEN  EXERCISE 

Copy,  and  insert  the  missing  numbers : 

1.  5  +  *  =  9,      6.+  *  =  9,     4  +  *  =  8,     3  +  *  =  8. 

2.  2  +  *  =  10,    7  +  *=10,  6  +  *  =  10,  4  +  *  =  10. 

3.  7-*  =  4,    10-*  =  3,     9-*  =  5,     8-*  =  3. 

4.  2  x  *  =  4,    2   times  *  spheres  =  4    spheres,    3 
times  *  spheres  =  6  spheres. 

5.  2  spheres  and  2  spheres  and  2  spheres  are  * 
spheres. 

6.  2  times  *  of  a  sphere  =  1  sphere,  4  times  *  of  a 
sphere  =  1  sphere,  3  times  *  of  a  sphere  =  1  sphere. 


26  PRIMARY  ARITHMETIC 

MEASURES 
ORAL   EXERCISE 

1.  How  many  feet  in  1  yard? 

2.  Measure  the  length  of  the  room  in  yards. 

3.  If  a  table  is  2  yards  long,  it  is  how  many  feet 
long? 

4.  How  many  feet  are  there  in  1  yard  and  2 
feet  ?  in  3  yards  ? 

5.  How  many  inches  are  there  in  1  foot  ?  in  1 
foot  less  2  inches  ? 

6.  How  many  feet  are  2  feet  +  2  feet  +  2  feet  ? 
How  many  yards  ? 

7.  State  quickly  the  value  of   each  of  the  fol- 
lowing : 

6  feet  —  4  feet  6  yards  -  4  yards 

6  inches  —  4  inches  2  times  2  inches 

2  times  2  yards  2  times  2  feet 

^  of  3  feet  ^  of  8  paces 

• 

8.  If  you  are  1  yard  and  1  foot  tall,  how  many 
feet  tall  are  you  ? 

9.  If  your   desk  lacks  1  foot  of  being  a  yard 
long,  how  many  feet  long  is  it? 

Pupils  should  have  abundant  exercise  in  measuring  lines,  in 
comparing  lengths,  and  in  finding  how  much  longer  one  line  is 
than  another.  Not  only  should  every  school  be  supplied  with  the 
common  measures,  but  children  should  be  entirely  familiar  with 
them  through  frequent  use. 


LENGTH  27 

You  have  now  learned  that 

12  inches  =  1  foot. 
3  feet       =  1  yard. 

We  usually  write  in.  for.  inch  or  inches,  ft.  for  foot 
or  feet,  yd.  for  yard  or  yards,  2  ft.  3  in.  for  2  feet  and 
3  inches. 

ORAL  EXERCISE 

1.  2  ft.  +  3  ft.  4-  6  ft.  2.  3  yd.  +  4  yd.  +  5  yd. 
3.  7  ft.  -  3  ft.  -  2  ft.  4.  12  in.  -  4  in.  -  5  in. 
5.  £  of  3  yd.  6.  J  of  4  yd.  7.  |  of  5  yd. 

WRITTEN   EXERCISE 

Find  the  sums  in  Exs.  1-5 : 

1.  4  2.  2  3.   1  4.  6  5.  1 

232  1  2 

3  1  412 

12122 


Ae  differences  in  Exs.  6-10 : 

6.  6  7.  10          8.  7          9.  8  10.   9 

2  _3  4  5  2 

Copy  Jfos.  ll-l^  and  write  the  answers: 

11.  £  of  8  blocks.         12.  £  of  6  blocks. 
13.  |  of  8  cents.  14.  £  of  6  marbles. 

15.  Make    10   little   stars    on   your    paper    and 
draw  a  line  around  half  of  them.     How  many  is 
of  10  ? 


28  PKIMARY    ARITHMETIC 

ORAL  EXERCISE 

1.  How  many  cents  make  a  nickel?  a  dime? 

2.  Tell  me  something . that  cost  you  a  nickel; 
a  dime. 

3.  How  many  nickels  make  a  dime?     A  nickel 
is  what  part  of  a  dime? 

4.  A  cent  is  what  part  of  a  nickel?     A  cent  is 
what  part  of  a  dime? 

5.  How  many  dimes  make  a  dollar?     A  dime  is 
what  part  of  a  dollar? 

You  have  now  learned  that 

5  cents    =  1  nickel. 
1C  cents    =  1  dime. 
1O  dimes  =  1  dollar. 

We  usually  write  ct.  or  p  for  cent  or  cents,  $2  for  2 
dollars. 

Every  school  should  be  supplied  with  toy  or  real  money,  and 
the  pupils  should  be  given  exercises  in  buying,  selling,  arid 
making  change.  Children  should  know  that  a  denomination 
applying  to  the  first  number  of  a  column  in  addition  or  sub- 
traction, like  the  ct.  in  the  written  exercise  below,  applies  to  the 
numbers  that  follow. 

WRITTEN  EXERCISE 


Add: 

1.  2  ct. 

2.  3  ct. 

3.  4  ct. 

4.  6  ct. 

5.  2  ct. 

3 

1 

2 

1 

2 

1 

1 

1 

1 

2 

4 

2 

1 

2 

2 

MEASURES 


ORAL  EXERCISE 
HELEN  WEAVES  A  RUG 

1.  Helen  had  3  skeins  of  black  and  2  of  orange 
wool.     How  many  skeins  of  wool  had  she  ? 

2.  The  wool  cost  2  ct.  a  skein.     How  much  did 
the  orange  wool  cost  ?     How  much  did  all  of  the 
wool  cost  ? 

3.  She  used  3  skeins  of  black 
and  1  of  orange  for  this  rug.  How 
many  skeins  had  she  left  ? 

4.  There  are  6  in. 
of  black  and  2  in. 
of  orange  in  the 
rug.    How  long 

is  the  rug  ? 

5.  If  she  wove    m 
2  in.  of  the  rug 
each   day,    how 
many  days   did 

it  take  her  to  make  it? 

6.  If  Helen  puts  a  1-in.  fringe  on  each  end,  how 
much  longer  will  the  rug  be  ? 

7.  If  she  makes  4  tassels  for  each  end,  how  many 
tassels  will  she  make  ? 

8.  If  she  weaves  3  rows  of  orange  in  each  bor- 
der, how  many  will  there  be  in  the  two  borders  ? 

9.  If  the  rug  is  10  in.  long  and  6  in.  wide,  it  is 
how  much  longer  than  wide  ? 


'60 


PRIMARY   ARITHMETIC 


ORAL  EXERCISE 

1.  Which    is   the  pint  measure  in  the  picture, 

and  which  is  the 
quart  ? 

2.  How  many 
pints    make    a 
quart  ?     A  pint 
is  what  part  of 
a  quart  ? 

3.  Can  you 
tell  me  several 
things  that  are 
sold  by  the  pint 
and  by  the  quart? 
What  are  they  ? 

4.  How  much  does  a  quart  of  milk  cost  ?  a  pint  ? 

5.  If  I  have    a  quart  of  cream  and  a  pint  of 
cream,  how  many  pints  do  I  have? 

6.  Draw  on  the  blackboard  a  full-size  picture  of 
a  quart  measure.     Draw  a  line  across,  marking  off 
1  pint. 

In  all  oral  work,  of  which  this  is  merely  a  specimen,  the  prob- 
lems should  be  made  to  appeal  to  the  children's  daily  interests  as 
far  as  possible,  and  the  actual  measures  should  be  used. 

You  have  now  learned  that 

2  pints  =  1  quart. 

We  usually  write  pt.  for  pint  or  pints,  and  qt.  for 
quart  or  quarts. 


WEIGHT 


31 


ORAL  EXERCISE 

1.  The  children  in  the  picture  have  a  2-pound 
weight    and    a     

|-pound  weight 
to  balance  the 
book.  Tell  me 
how  much  the 
book  weighs. 

2.  If     they 
should    weigh 
1  pt.  of  water, 
they  would  find 

that  it  weighs  a  pound.    How  much  does  1  qt.  weigh? 

3.  If  one  of  your  books  weighs  ^  pound,  another 
|  pound,  and  another  ^  pound,  how  much  do  all 
three  weigh  ? 

4.  If  the  children  had  a  pound  of  figs  worth  2 
dimes,  how  much  would  J  pound  be  worth  ? 

5.  Multiply  the  following  by  2  and  add  1  pound 
to  each  result : 

1  pound  2  pounds         3  pounds 

6.  Find  J  of  each  of  the  following : 

4  pounds         2  pounds         6  pounds 

We  usually  write  Ib.  for  pound  or  pounds. 

It  is  desirable  that  children  should  weigh  various  objects,  using 
the  pound,  half  pound,  and  quarter  pound.  The  ounce  may  be 
introduced  here,  although  it  is  taken  up  when  this  topic  is  next 
discussed,  on  page  56. 


CHAPTER  II 

I.    REVIEW  OF  NUMBERS  TO  100 
COUNTING 

10          20  30          40  50 

60          70          80          90        100 

ORAL  EXERCISE 

1.  How  many  books  are  there  in  the  picture? 
If  there  were  10  more,  how  many  would  there  be  ? 


2.  How  many  blocks  in  the    black  and  white 
pile?     How  many  10's  in  this  pile? 

3.  There  are  3  columns  of  smaller  blocks.     How 
many  blocks  in  each  column  ?     How  many  in  all  ? 

4.  There  are  4  bundles  of  splints  in  the  picture, 
10  in  each  bundle.     How  many  splints  in  all? 

5.  There  are  5  packages  of  envelopes,  10  in  each 
package.     How  many  envelopes  are  there  ? 

32 


COUNTING   BY   TENS  33 

ORAL  EXERCISE 

1.  If  you  call  2  tens  twenty,  and  write  it  20,  and 

3  tens  thirty,  and  write  it  30,  what  should  you  call 

4  tens,  and  how  should  you  write  it  ?     The  same 
f  i.rj.       *      ^>       *       o       o        i        o        » 

111111111 

2123456789 
3       5  tens       30       40       50       60       20 

3.  How  much  is  i  of  10  ?     £  of  10  tens  ?     1  of 
100  ?     How  many  cents  in  J  of  100  cents  ? 

One  half  of  a  dollar  is  5O  cents. 

4.  Subtract  rapidly : 

5   5  tens   50   70   90   90   60 
2   2  tens   20   30   40   30   40 

5.  Multiply  rapidly : 

2       2  tens       20       10       10       10       10 
2       2 _2       _2       _3       _4       _7 

In  the  above  work  teachers  may  find  it  of  advantage  to  place 
columns  of  10's,  20's,  and  30's  011  the  board,  similar  to  the  columns 
of  2's  and  3's  on  page  15. 

WRITTEN  EXERCISE 

1.  Write  in  figures  :  thirty,  seventy,  fifty,  ninety, 
sixty,  eighty,  one  hundred. 

2.  Write  in  words :  10,  60,  100,  90,  80,  20,  40. 


34  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  Point  to  10  splints  and  3  splints  in  the  picture. 
How  much  is  10  +  3?     Write  the  number  on  the 
blackboard. 

I.    REVIEW  OF  NUMBERS  TO  100 

COUNTING 

2.  In  the  second  group,  how  many  packages  of 
10  splints  each,  and  how  many  splints  over  ?   Write 
the  number.     Do  this  for  the  other  groups. 

Let  the  children  make  bundles  of  splints,  but  do  this  only 
until  the  idea  is  clear.  After  that  the  objects  become  harmful. 

3.  Read  the  numbers  : 

15        21        32        48        56        60 
35        65        78        83        90         99 

4.  How  many   days    in   this   month?     This   is 
what  day  of  the  month? 

5.  Count  the  children  in  your  class;  the  desks 
in  your  room ;  the  panes  of  glass  in  the  windows. 

These  are  merely  suggestive  of  other  counting  exercises.  In 
schools  where  a  record  of  temperature  is  kept,  pupils  may  read 
the  thermometer  daily  and  write  the  record  on  the  board. 

In  the  number  25  we  speak  of  the  5  as  units,  the  2 
as  tens. 

WRITTEN  EXERCISE 

Write  twenty-seven,  seventy-nine,  'sixty-eight, 
forty-two,  eighty,  ninety-four. 


ADDITION 


35 


ADDITION 

ORAL  EXERCISE 

Revieiv  rapidly 

the  follmving  : 

1. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

2 

2 

2 

2 

2. 

2 

2 

2 

2 

3. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

3 

3 

3 

3 

3 

3 

3 

3 

3 

4. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

4 

4 

4 

4 

4 

4 

4 

4 

4 

5. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

5 

5 

5 

5 

5 

5 

5 

5 

5 

6. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

6 

6 

6 

6 

6 

6 

6 

6 

6 

7. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

7 

7 

7 

.  7 

7 

7 

7 

7 

7 

8. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

8 

8 

8 

8 

8 

8 

8 

8 

8 

9. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

This  table  should  be  reviewed  frequently. 


PRIMARY   ARITHMETIC 


ORAL  EXERCISE 

Find  the  sums  in  Exs.  1-2: 


1. 

4 

14 

34  ' 

5 

25 

56 

7 

17 

2 

2 

2 

3 

_3 

1 

_2 

_2 

2. 

47 

97 

3 

63 

83 

3 

53 

83 

2 

2 

4 

4 

4 

6 

6 

6 

Find  the  sums  in  Exs.  3-8,  stating  first  the  units, 
then  the  tens,  then  the  answer : 

3.   1       4.   10       5.   10       6.   10       7.   12       8.   16 

2  20  3  23  20  30 

3  30  _5  35  34          40 

9.  How  much  is  5  +  5?     54-5  +  5  +  5? 
10.  How  much  is  25  +  25  +  25  +  25  ?    Then  how 
much  is     of  100  ? 


A  quarter  of  a  dollar  is  25  cents. 

11.  If  the  square  is 

D 


called  1,  one  oblong 
is  10  and  the  other  4. 
What  are  the  two  together  ? 


1 


r? 


12.  These  oblongs  show  what  numbers  ? 

Teachers  will  find  it  helpful  to  use  paper  rectangles  like  these 
to  explain  addition  and  subtraction. 


ADDITION  37 

ORAL  EXERCISE 
BEAN-BAG  SCORE 

Elsie,  Clyde,  and  Frank  played  throwing  bean  bags 
into  the  rings  to-day.  A  bag  in  the  outer  ring  counts  1; 
one  in  the  inner  ring  counts  3. 

1.  Elsie  threw  2  bags  in  the  inner  ring  and  also 

1  in  the  outer 
ring.  What  was 
her  score  ? 

2.  Then   she 
threw  1  in  the 
inner  ring  and 

2  in  the  outer 
one.  What  was 
her  score  then  ? 

3.  The  third 

time  she  threw,  1  went  in  the  inner  ring,  1  in 
the  outer  ring,  and  1  did  not  go  in  either.  What 
was  her  score  then?  Write  her  scores  on  the 
blackboard  and  add. 

4.  Clyde's  first  throw  was  3  in  the  inner  ring. 
The  second  was  2  in  the  inner  ring  and  1  outside 
of  both  rings.     The  third  was  1  in  the  inner  ring 
and  the  other  2  outside  of  both  rings.     How  much 
did  he  make  in  all  ? 

5.  Frank's  score  was  3  and  0.     He  then  threw 

3  in  the  inner  ring.     What  was  his  total  score? 
Who  beat  in  the  game  ? 


38  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 
OTHER  NUMBER  GAMES 

1.  Laura  and  Marion  threw  bean  bags  through 
a  hanging  hoop  in  which  was  a  bell.     Every  bag 

that  went  through  without  ringing  the 
bell  counted  10.  If  the  bell  rang,  the 
throw  counted  only  2.  In  ten  throws 
each,  the  score  was : 

Laura,      0,0,2,10,0,0,2,2,    0,10; 
Marion,  10,  0,  0,    0,0,2,0,0,10,    2. 

What  was  the  score  of  each?    Which 
won  the  game  ? 

2.  Ned  and  Jack  cut  holes  in  the  bottom  of  a 
cardboard   box,  like   this.      They   numbered   the 
largest  1,  the  next  3,  the 

next  5,  the  next  7,  and 

the  smallest  10.     They 

put  the  box  on  the  floor 

and  dropped  marbles  from  the  height  of  a  table 

With  10  marbles  each,  the  score  was :  * 

Ned,    1,    1,    3,    1,    0,    10,    7,    5,    0,      1 ; 

Jack,  0,   5,   0,   1,   1,     1,    1,   7,   7,   10. 

What  was  the  score  of  each  ? 

These  and  ringtoss  are  merely  suggestive  of  number  games 
that  children  may  be  encouraged  to  play,  the  work  being  entirely 
oral.  Many  simple  games  of  this  kind  can  be  bought  at  toy 
stores. 


ADDITION 


39 


WRITTEN  EXERCISE 


Add  the  following : 


1. 

23   2.  42   3.  29 

4. 

35   5.  61   6. 

33 

32     50     60 

44     27 

44 

7. 

23   8.  34   9.  24 

10. 

22   11.  12  12. 

16 

42     25     40 

33     41 

10 

3     30     35 

43     15 

32 

13. 

22  14.  23   15.  13 

16. 

26  17.  25  18. 

12 

31     40     21 

42     30 

13 

14     6     44 

11     20 

41 

11     10     10 

10     _2 

10 

19. 

12  20.  26  21.  33 

22. 

41  23.  33  24. 

11 

20     31     32 

4     23 

22 

3     11      3 

2     30 

33 

2     10     10 

20      2 

2 

41     20     10 

11     10 

20 

25. 

4  +  3  +  11  +  0  +  21. 

26. 

20  +  10  +  1  +  2  +  3. 

27. 

30  +  3  +  40+4  +  1. 

28. 

10  +  22  +  4  +  1  +  2. 

29. 

20  +  2  +  20  +  2  +  2. 

30. 

30  +  11  +  2  +  1  +  3. 

31. 

60  +  10  +  4  +  1  +  2. 

32. 

40  +  20  +  3  +  5  +  1. 

33. 

30  +  20  +  5  +  2  +  1. 

34. 

2  +  2  +  3  +  4  +  5  +  7. 

35. 

3  +  2  +  5  +  1  +  0  +  8. 

36. 

4  +  1  +  0  +  6  +  2  +  3. 

37. 

2  +  6  +  3  +  5  +  1  +  2. 

38. 

3  +  2  +  4  +  1  +  7  +  5. 

39. 

6  +  2  +  1  +  2  +  3+4. 

40. 

2+4  +  3  +  1  +  3  +  2. 

41. 

5  +  5  +  2  +  2  +  1  +  1. 

42. 

2  +  2  +  4  +  4  +  1  +  2. 

43. 

6  +  4  +  7  +  3  +  8  +  2. 

44. 

14  +  10  +  21  +  20  +  11. 

40  PRIMARY   ARITHMETIC 

WRITTEN  EXERCISE 

1.  There  are  15  apples  in  one  pile  and  21  in 
another ;  how  many  in  both  piles  ? 

2.  Mary  has  17  ct.,  and  she  earns  21  ct.?  and 
her  father  gives  her  10  ct.     How  much  has  she? 

3.  Kate  has  28  chickens,  and  Mollie  has  20 ; 
how  many  have  they  together? 

Make  problems  for  Exs.  4~17?  an&  find   ^e 
answers : 

4.  2  ct.  +  3  ct.  +  5  ct.      5.  3  qt.  +  2  qt.  +  1  qt. 
6.  2  ft.  +  4  ft.  +  15  ft.     7.  3  Ib.  +  6  Ib.  +  40  Ib. 
8.   $2  +  $5  +  $7  +  $1.     9.  4  Ib.  +  2  Ib.  +  71  Ib. 

10.  4  +  24-3  +  54-2  +  1. 

11.  6  +  4  +  2  +  3  +  5  +  1. 

12.  $14 +  $2 +  $20 +  $2. 

13.  $14  +  $30 +  $1  + $20. 

14.  $21 +  $30 +  $15 +  $2. 

15.  21  boys  +  3  boys  +  14  boys. 

16.  12  girls  +  3  girls  +  22  girls. 

17.  4  marbles  +  11  marbles  +  32  marbles. 

Add  the  following  : 


20 

19.  12 

20.  21 

21.  12 

22.  51 

23.  13 

11 

2 

21 

3 

3 

12 

13 

30 

21 

20 

2 

11 

22 

3 

21 

2 

2 

10 

10 

40 

12 

10 

20 

1 

11 

2 

12 

30 

20 

2 

SUBTRACTION  41 

SUBTKACTIOJST 

ORAL   EXERCISE 

Subtract,  stating  first  the  units,  then  the  tens : 

I.  9   2.  90   3.  99   4.  96   5.  87   6.  76 

3  30     33     32     43     32 

7.  7   8.  70   9.  77  10.  78  11.  87  12.  75 

4  40     44     42     34     22 

WRITTEN   EXERCISE 

Copy  the  following  and  subtract: 
1.  98      2.  89      3.  93      4.  64       5.  55       6.  63 
73          46  31  24  21  52 

7.  82      8.   78      9.  65     10.  53      11.  31     12.  29 
50          37          52  12  11  18 

ORAL  EXERCISE 
SOME  OF  YOUR  PURCHASES 

1.  If  you  pay  35  ct.  for  a  book,  and  5  ct.  for  a 
pencil,  how  much  do  both  cost  ? 

2.  If  you  give  the  merchant  half  a  dollar  for 
them,  how  much  change  should  you  receive  ? 

3.  How  much  must  you  add  to  this  change  to 
have  enough  to  buy  a  15-ct.  drawing  book? 

4.  If  you  pay  12  ct.  for  candy,  and  5  ct.  for  an 
orange,  how  much  do  you  pay  for  both  ? 


42  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  How  much  will  a  10-ct.  ball  and  15  ct.  worth 
of  marbles  cost  ? 

2.  John  is  7  years  old,  and  is  4  years  older  than 
his  sister.     How  old  is  his  sister  ? 

3.  If  Mary  has  a  10-ct.  piece,  a  5-ct.  piece,  and 
three  1-ct.  pieces,  how  much  money  has  she  ? 

4.  Helen  had  42  ct.  in  her  bank,  and  her  aunt 
gave  her  10  ct..  more.     How  much  money  had  she 
then? 

5.  In  our   class  there  are  29  children.     In  the 
class  below  there  are  5  less.     How  many  are  in 
that  class  ? 

6.  There  are  15  men  in  a  band.     One  plays  the 
bass  drum,  1  plays  the  small  drum,  and  the  rest 
play  horns  or  fifes.    How  many  play  horns  or  fifes  ? 

Teachers  usually  find  it  interesting  to  children  to  let  them 
occasionally  make  their  own  oral  problems. 

WRITTEN  EXERCISE 

1.  If  one  class  has  28  children  and  another  has 
12  less,  how  many  are  in  the  other  class  ? 

2.  If  there  are  22  in  one  class  and  15  more  in 
another  class,  how  many  are  in  the  other  class  ? 

3.  If  there  are  41  children  in  one  class  and  34 
in  another  class,  how  many  are  in  both  classes  ? 

4.  If  you  should  pay  40  ct.  for  a  book,  15  ct. 
for  a   tablet,  and  2  ct.  for   a   pencil,  how  much 
would  you  pay  for  all? 


SUBTRACTION  43 

WRITTEN  EXERCISE 

Subtract: 

1.  39   2.  28   3.  92   4.  48   5.  61   6.  86 
17     16     71     32     20    _5 

7.  47   8.  37   9.  48   10.  69   11.  81   12.  77 
16     21     37     34     20    J5 

13.  59   14.  78  15.  37  16.  29  17.  82  18.  37 
16     17     21     19     22     27 

19.  40   20.  62   21.  48  22.  72   23.  89  24.  43 
30     50     38     60     _J9     10 

25.  79   26.  28  27.  49  28.  53  29.  63  30.  44 
49     17     29     33     23     32 

31.  37-16.  32.  42-12.  33.  67-42.  34.  29-12. 

35.  88-42.  36.  79-63.  37.  88-22.  38.  99-29. 

39.  97-26.  40.  87-73.  41.  61-41.  42.  72-62. 

43.  49-19.  44.  69-58.  45.  98-65.  46.  92-50. 

47.  77-44.  48.  95-14.  49.  83-31.  50.  59-37. 

51.  87-72.  52.  85-23.  53.  87-21.  54.  78-30. 

55.  91-20.  56.  71-40.  57.  61-10.  58.  82-20. 

59.  53-23.  60.  67-66.  61.  74-34.  62.  92-91. 

63.  85-24.  64.  69-35.  65.  47-27.  66.  53-13. 

67.  How  much  is  77  minus  53?    48  minus  30? 

68.  What  number  added  to  23  makes  89? 

69.  What  number  subtracted  from  56  leaves  23  ? 

70.  What  is  the  difference  between  98  and  27? 


44  PRIMARY   ARITHMETIC 

WRITTEN  EXERCISE 

1.  Eloise  has    75  ct.    and  spends  34  ct.      How 
much  has  she  left? 

2.  Ralph  had  18  papers  to  sell;  he  has  sold  12. 
How  many  has  he  left? 

3.  There  were  48  apples  in  a  basket;  27  have 
been  taken  out.     How  many  are  left? 

Make  problems  for  Exs.  ^-18,  and  find  the 
answers : 

4.57-26.                5.29-13.  6.75-15. 

7.95-25.  8.68-24.  9.73-20. 

10.  25  ft.  -  4  ft.  11.  75  ct.  -  5  ct.  12.  72  - 10. 

13.  75  ct.  -  25  ct.  14.  78  ft.  - 16  ft.  15.  82  -  30. 

16.  15yd.-12yd.  17.  90 yd. -20 yd.  18.62-20. 

Find  the  missing  numbers  in  Exs.  19-54  '• 

19.  15  +  *  =  18.  20.  23  +  *  =  29.  21.  35  +  *  =  49. 

22.  22  +  *  =  59.  23.  37  +  *  =  97.  24.  41  +  *  =  83. 

25.  27  +  *  =  87.  26.  13  +  *  =  86.  27.  40  +  *  =  98. 

28.  *  + 14  =  75.  29.  *  + 23  =  49.  30.  *  + 81  =  92. 

31.  62-*  =  60.  32.  75-*  =  72.  33.  87-*  =  83. 

34.  28-*  =  15.  35.  67-*  =  37.  36.  71-*  =  31. 

37.  73  -  *  =  20.  38.  98  -  *  =  75.  39.  99  -  *  =  66. 

40.  *- 15  =  60.  41.  *- 20  =  33.  42.  *- 45  =  10. 

43.  *  -  11  =  27.  44.  *  -  12  =  35.  45.  *  -  22  =  17. 

46.    5  +  *  =  85.  47.  23  +  *  =  99.  48.  18  +  *  =  89. 

49.  *  + 57  =  78.  50.  71-*  =  70.  51.  62-*  =  41. 

52.  93-*  =  31.  53.  *- 70  =  11.  54.  *- 30  =  21. 


MULTIPLICATION  45 

MULTIPLICATION 

ORAL  EXERCISE 

1.  Add  2  ct.  and  2  ct.     Then  how   many  are 
2  times  2  ct.  ? 

2.  How  many  are  2  times  $3  ?    2  times  4  inches  ? 
2  times  5  pounds  ?   2  times  $6  ? 

3.  How  many  are  three  2's?  three  3's?  three  4's? 
Draw  pictures  to  explain  your  answers. 

4.  How  many  are  four  2's  ?          II     II     II     II 
How  many  are  four  3's  ?   How        III     III     III     III 
many  are  five  2's?   How  many       II     II     II     II     II 
are  six  2's?  II     II     II     II     II     II 

5.  How  many  are  two  4's  ?   three  4's  ?   two  5's  ? 
two  6's  ? 


Learn  these  : 

2  twos  =    4 

2  threes  =    6 

2  fours  =    8 

3  twos  =    6 

3  threes  —    9 

3  fours  -  12 

4  twos  =    8 

4  threes  =  12 

2  fives  =  10 

5  twos  =  10 

6  twos  =  12 

2  sixes  =  12 

6.  How  many  are  3  times  3  ?   3  times  3  tens  ? 
3  times  30  ?   4  times  20  ? 

7.  How  many  are  5  times  2  tens  ?    5  times  20  ? 
2  times  30  ?   3  times  30  ? 

8.  Multiply : 

f  3        3  tens      30       30  +  1        31        32 

22  2  222 


46  PRIMARY   ARITHMETIC 

DIVISION 
ORAL   EXERCISE 

1.  How  many  twos  do  you  see  in  4?          II 

2.  How  many  twos  do  you  see  in  6  ?         1 1  1 
How  many  threes  ? 

3.  How  many  twos  do  you  see  in  8  ? 
How  many  fours? 

4.  How  many  fours  are  there  in  12? 

How  many  sixes?     Show  this  on  the  blackboard 

Learn  these : 

4-2  =  2  12-2  =  6  8-4  =  2 

6-2  =  3  6-3  =  2  12-4  =  3 

8-2  =  4  9-3  =  3  10-5  =  2 

10-2  =  5  12-3  =  4  12-6  =  2 

We  shall  later  write  6  -f-  3  =  2  like  this :  2)6 

Your  teacher  may  have  you  write  it  so  now.  3 

5.  How  much  is  4 -2?   40-2?   60-2? 

6.  How  much  is  6-3?   60-3?   90-3? 

7.  How  much  is  J  of  40?    of  60?    of  80?    of 
100? 

8.  How  much  is  J  of  60?    |  of  90?    |  of  80? 

9.  If  line  a  represents  20,  what  does  b  repre- 
sent?    If  b  represents  20,  what   a 

does  a  represent? 

10.  If    b   represents    20,    what   d- 
does  c  represent  ?     If  c  represents  20,  what  does  b 
represent?  dl  a? 


DIVISION  47 

ORAL  EXERCISE 
SOME  PURCHASES  FOR  THE  HOME 

1.  When  peaches  are  selling  for  10  ct.  a  quart, 
how  much  will  2  qt.  cost  ? 

2.  When  milk  costs  6  ct.  a  quart,  how  much  will 
Ipt.  cost?   3pt.?   2  qt.? 

3.  When  cream  costs  40  ct.  a  quart,  how  much 
will  1  pt.  cost?     (Think  of  £  Of  4,  then  £  of  40.) 
How  much  will  ^  pt.  cost  ? 

4.  When  sugar  is  selling  at  8  ct.  a  pound,  how 
much  will  ^  pound  cost  ?   ^  pound  ? 

5.  Suppose  Kate  wishes  to  serve  some  peaches 
and  cream  to  her  friends,  and  uses  1  qt.  of  peaches, 
\  pt.  of  cream,  and  \  pound  of  sugar ;  at  the  prices 
given,  how  much  will  the  peaches,  cream,  and  sugar 
cost  ?     (Write  on  the  blackboard  and  add.) 

WRITTEN  EXERCISE 

1.  Copy  the  following  and  write  the  results : 

I-  of  6          i  of  60          i  of  6          i  of  60 
i  of  6 
\  of  8 

2.  Add 


JUl 

fof 

UU 

80 

f  01  0 

iof  8 

^-  UJ.  OU 

$  of  80 

20  ct. 

30  Ib. 

60  qt. 

$22 

30 

20 

10 

13 

40 

10 

5 

31 

2 

5 

1 

10 

3 

4 

2 

2 

48  PRIMARY  ARITHMETIC 

NUMBER  TABLE 

0  10  20  30  40  50  60  70  80  90 

1  11  21  31  41  51  61  71  81  91 

2  12  22  32  42  52  62  72  82  92 

3  13  23  33  43  53  63  73  83  93 

4  14  24  34  44  54  64  74  84  94 

5  15  25  35  45  55  65  75  85  95 

6  16  26  36  46  56  66  76  86  96 

7  17  27  37  47  57  67  77  87  97 

8  18  28  38  48  58  68  78  88  98 

9  19  29  39  49  59  69  79  89  99 

The  table  should  be  written  upon  the  blackboard. 
ORAL   EXERCISE 

1.  Point    to  the  line  of  numbers  less  than  10. 
If  you  add  10  to  each,  which  line  have  you? 

2.  Point  to  the  line  of  10's.     If  you  add  1  to 
each  number,  which  line  have  you?     If  you  add 
1  more  ? 

3.  Of  the  numbers  below  100,  how  many  end  in 
9  ?     Point  to  them.     How  many  end  in  8  ? 

4.  How  many  columns  are  there  ?     How  many 
numbers  in  a  column?     Then  how  many  numbers 
in  all,  including  0  ? 

5.  Count  by  10's,  beginning  with  0;  beginning 
with  1 ;  beginning  with  2 ;  with  3. 

The  above  table  offers  many  opportunities  for  oral  work,  as  in 
counting  by  9's  and  ll's,  adding,  and  performing  other  operations. 


TIME 


49 


TIME 

ORAL   EXERCISE 

1.  Read  the  figures,  or  numerals,  on  the  clock. 

2.  Which  hand  tells  the  hours  ?  the  minutes  ? 

3.  How  long  does  it  take 
the  hour  hand  to  pass  from 
I  to  II  ?    How  long  does  it 
take  the  minute  hand  ? 

4.  How    long    does     it 
take  the  hour  hand  to  pass 
around  from   XII  to   XII 
again  ?  the  minute  hand  ? 

5.  What   time  is  it   by 

the  clock  in  the  picture  ?   by  the  school  clock  ? 

6.  How  many  minutes  in  an  hour  ?   in  ^  hour  ? 
How  many  hours  in  a  day,  including  the  night  ? 

The  figures  on  clocks  are  such  as  the  Romans  used 
long  ago.  Our  numerals  were  brought  from  India  by  the 
Arabs.  The  Roman  and  Arabic  numerals  to  twelve  are: 

I,  II,  III,  IIII  or  IV,  V,  VI,  VII,  VIII,  IX,  X,  XI,   XII. 
1,  2,     3,  4,         5,    6,       7,       8,       9,    10,  11,     12. 

You  have  learned  that 

6O  minutes  =  1  hour. 

24  hours       =  1  day. 

We  usually  write  min.  for  minute  or  minutes, 
hr.  for  hour  or  hours,  da.  for  day  or  days,  A.M.  for 
forenoon,  P.M.  for  afternoon. 

We  write  15  minutes  after  2  like  this,  2:15. 


50  PRIMARY   ARITHMETIC 

THE   DOZEN 

ORAL   EXERCISE 

1.  How  many  cubes  make  a  dozen? 

2.  What  other   name  can  you  give  to  a  dozen 
inches  ? 

3.  Name  some  things  that 
are  .sold   by    the   dozen.     At 
what  price? 

4.  How  many  cubes  make 
a  half  dozen?   a  quarter  of  a 

dozen  ?   a  third  of  a  dozen  ?     Point  to  them. 

5.  How  many  fours    do   you  see  in  a  dozen? 
How    many   threes  ?      How  'many   twos  ?      How 
many  sixes  ?     Point  to  them. 

6.  A  hen  sits  on  a  dozen  eggs  and  hatches  all 
but  two.     How  many  chickens  are  hatched  ? 

7.  When  eggs   are  worth  20  ct.  a  dozen,  how 
much  does  a  half  dozen  cost? 

8.  A  newsboy  buys  a  dozen  papers  for  8  ct.?  and 
sells  them  at  a  cent  apiece.     How  much  does  he 
make  ? 


9.  John  had  a  dozen  firecrackers.  When  they 
were  lighted,  all  but  \  of  them  exploded.  How 
many  firecrackers  exploded? 

We  usually  write  doz.  for  dozen. 


READING   AND   WRITING   NUMBERS 


51 


II.    NUMBERS  TO  1000 
READING  AND  WRITING  NUMBERS 

ORAL  EXERCISE 

1.  Here  are  4  bundles  of  splints,  10  in  a  bundle. 
How    many    splints 

are  there?  Write  the 
number  on  the  black- 
board. 

2.  Here  are  3  bundles  of  splints,,  100  in  a  bun- 

dle. How  many  splints 
are  there  ?  Write  the  num- 
ber on  the  blackboard.  If 
there  were  400  more,  how 
many  would  there  be? 
Write  the  number. 

3.  Here  is   a   larger   bundle 
of  splints,  as    many  as   in   10 
bundles    of    100    each.      How 
many  splints  are  there  in  this 
bundle  ?      Write    the    number 
on  the  blackboard. 


WRITTEN  EXERCISE 


1.  Write  in  figures  the   numbers  one  hundred, 
six  hundred,  nine  hundred,  one  thousand. 

2.  Write  in  words  the  names  of  these  numbers: 


300 


700       50       1000       600        75 


52  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  Count  by  100's  from  100  to  1000. 

2.  Add  rapidly : 

2  20      22      200      6      60      66      600 

3  30      33      300      3      30      33      300 

In  such  cases  the  numbers  should  be  written  on  the  blackboard. 

3.  Subtract  rapidly: 

7   70   77   700   9   90   99   900 

4  4Q   44   4QQ   2   20   22   200 

4.  Multiply  rapidly: 

1      10      3      30      33      300      40      400 

_2      _2      2      _2      _2       _2      _2       _2 

5.  Tell  rapidly  the  values  of  J  of  4,  £  of  40,  £  of 
400,  £  of  3,  £  of  30,  I  of  300. 

6.  If  John  had  200  yards  of  kite  string  and  lost 
J  of  it,  how  much  would  he  have  left  ? 

7.  If  there  are  100  firecrackers  in  a  bunch,  how 
many  are  there  in  3  bunches?   in  10  bunches? 

8.  If  you  take  600  steps  in  walking  from  one 
street  corner  to  the  next,  how  many  steps  will  you 
take  in  walking  half  this  distance? 

WRITTEN   EXERCISE 

Write  the  numbers  from  1  to  9;  below  them, 
the  10's  from  10  to  90 ;  below  these,  the  100's  from 
100  to  900. 


COUNTING 


53 


300 


+  40 


ORAL  EXERCISE 

1.  How  many  splints  are  there  in  the  picture? 

2.  Read  the  numbers: 

342   352   362   372   392   312   302 

3.  Read  the  numbers : 

100  101  102  105  110  111  123 
200  202  203  205  220  222  234 
900  909  910  905  990  999  987 

4.  Open  this  book  to  page  147;  to  page  203. 

5.  The  numbers  below  10  are  called  units.     Do 
you  write  the  units  in  the  left-hand  or  in  the  right- 
hand  place?    Where  do  you  write  the  tens?   Where 
do  you  write  the  hundreds  ? 

6.  Name  the  figures  in  units'  place  in  475 ;  in 
tens'  place;  in  hundreds'  place. 

WRITTEN  EXERCISE 


1.  Write  in  figures: 
Five  hundred  fifty-five 
Two  hundred  forty-nine 
One  hundred  twenty-one 


Six  hundred  nine 
Three  hundred  three 
Eight  hundred  eighty 


2.  Write  in  words :   242,  307,  520,  634,  987. 


54  PRIMARY    ARITHMETIC 

ORAL  EXERCISE 

1.  Add  rapidly: 

1  10    100    110    111    123 

2  20    200    220    222    231 

3  30    300    330    333    312 

2.  Subtract  rapidly: 

7   70   700   770   777   777 
5    50    500    550    555    543 

George,  Will,  and  Kate  played  they  had  a  horse  show. 

3.  Ten   grown   people   came.     How   much   did 
they  all  pay  at  3  pins  each? 

4.  Twenty  children  came.    How  much  did  they 
all  pay  at  2  pins  each? 

5.  How  many  pins   in   all  were  taken  by  the 
doorkeeper? 

6.  The   doorkeeper   was    paid    10   pins.      How 
many  pins  were  left? 

WRITTEN  EXERCISE 

1.  Write    in    columns,  and  add  first  the  units, 
then  the  tens,  then  the  hundreds: 

312  +  234  +  412  423  + 102  +  361 

220  +  202  +  222  371  +  316  +  101 

2.  Write  in  columns  and  subtract: 

964  -  512         873  -  401 
796-514         985-472 


LENGTH  55 

MEASURES 
ORAL   EXERCISE 

1.  How  many  inches  in  1  ft.? 

2.  What  part  of    1  ft.  is  1  in.?    3  in.?   4  in.? 
6  in.? 

3.  How  many  feet  in  1  yd.  ?     1  ft.  is  what  part 
of  lyd.? 

4.  How  many  inches  in  %  ft.?  in  1J  ft.?  in  |  ft.? 
in  lift.? 

5.  How  many  inches  in  £  ft. ?  in  1£  ft.?  in  2  ft.? 
in  21  ft.? 

.6.  Measure  the  length  of  the  blackboard  in  feet 
and  inches. 

7.  How  many  inches    are  there  in  1  ft.  1  in.? 
1  ft.  2  in.?    1  ft.  4  in.?    1  ft.  6  in.?    1  ft.  8  in.? 
1ft.  10  in.? 

8.  Write  on  the  blackboard  what  you  think  is 
the  width  of  the  window  in  feet  and  inches.    Meas- 
ure and  see  if  you  are  right. 

WRITTEN  EXERCISE 

1.  Add: 

12  ft.   123  ft.   3  in.  12  ft.   123  ft. 
20    210     6     21    214 

2.  Subtract : 

39  ft.   439  ft.   10  in.  39  ft.   439  ft. 
10    210     7     14    214 


56  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  If  you  put  a  1-pound  weight  on  one  side  of 
the  scales,  do  you  know  how  many  ounce  weights 
must  be  put  on  the  other  side  to  balance  it? 

2.  Then    how    many    ounces    make    a    pound? 
Then  1  ounce  is  what  part  of  a  pound  ? 

If  there  are  scales  in  the  school,  children  should  weigh  various 
objects,  and  also  find  that  16  ounces  =  1  pound.  Children  some- 
times make  bags  of  different  sizes,  putting  in  enough  sand  to 
make  them  weigh  1  pound,  J  pound,  J  pound.  The  weights  are 
then  told,  the  children's  eyes  being  closed. 

You  have  found  that 

16  ounces  =  1  pound. 

We  usually  write  oz.  for  ounce  or  ounces,  Ib.  for  pound 
or  pounds. 

3.  The  average  height  and  weight  of  children  of 
your  age  is  about  as  follows : 

Boys  Girls  Boys  Girls 

7  yr.         44  in.        44  in.       48  Ib.        47  Ib. 

8  46  46  52  50 

9  50  49  57  55 

Compare  your  height  and  weight  with  the  average. 

WRITTEN  EXERCISE 

1.  Add  :  4  Ib.  +  5  Ib. ;  40  Ib.  +  50  Ib. ;  400  Ib. 
+  500  Ib. ;  423  Ib.  +  512  Ib. 

2.  Subtract :  9  Ib.  -  4  Ib. ;  90  Ib.  -  40  Ib. ;  900  Ib. 
-  400  Ib. ;  935  Ib.  -  423  Ib. 


WEIGHT  57 

ORAL  EXERCISE 

1.  How  many  small  squares  in  this  large  square  ? 
Half  are  white.    How  many  are  white  ? 

2.  Look  at  the  picture  and  see  J  of 
16;  1  of  16. 

3.  Then  how  many  ounces  in  ^  lb.? 
in  1  lb.? 

4.  How   many   pounds   is   J    of  12  lb.?     ^    of 
12  lb.? 

5.  When  sugar  is  6  ct.  a  pound,  how  much  does 
i  lb.  cost? 

6.  At  2  ct.  a  pound,  how  much  must  you  pay  for 
41b.  of  salt?   for  i  lb.? 

7.  At  7  ct.  a  pound,  how  much  must  you  pay 
for  10  lb.  of  oatmeal? 

8.  At  16  ct.  a  pound,  how  much  must  you  pay 
for  J  lb.  of  grapes?   for  |  lb.? 

WRITTEN  EXERCISE 

1.  If  you  weigh  44  lb.  7  oz. 
And  your  books  weigh  2         3 
The  total  weight  is  *  lb.   *  oz. 

2.  If  Charles  weighs  51  lb.  8  oz. 
And  his  dog  weighs              22 

And  his  books  2        4 

And  his  sled  10 

The  total  weight  is  *  lb.    *  oz. 


58  PRIMARY    ARITHMETIC 


WRITTEN  EXERCISE 


Add: 
1.  231 
322 
123 

2.  127   3.  225   4.  323 
621     502     270 
140      72     102 

5.  629 
30 
210 

6. 
11. 

120 

23 
4 
640 

7.  252   8.  121   9.  102 
104      32     571 
420      5     203 
12     400      12 

10.  400 

275 
102 
20 

201 
122 
141 

20 
3 

12.  123   13.  301   14.  101 

61      62     252 
400      13      21 
13     500     102 
201      12     202 

15.  521 

102 
20 
3 

2 

16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 

$121  +  $242  +  $103. 
33  in.  +  21  in.  +  324  in. 
107  ft.  +  621  ft.  +  30  ft. 
62  ft.  +  103  ft.  +  934  ft. 
$300  +  $62  +  $20  +  $4. 
125  Ib.  +  22  Ib.  +  230  Ib. 
204  Ib.  +  62  Ib.  +  122  Ib. 
21  yd.  +  200  yd.  +  75  yd. 
$20  +  $200  +  $2  +  $222. 
$6  +  $60  +  $600  +  $222. 
14  yd.  +  202  yd.  +  401  yd. 
$15  +  $150  +  $501  +  $111. 
$12  +  $120  +  $101  +  $333. 

ADDITION   AND  SUBTRACTION  59 


WRITTEN  EXERCISE 


1.  397-92. 
4.  546-32. 

7.  987-632. 

2.  486-75. 
5.  69,8-63. 
8.  798-345. 

3.  298-75. 
6.  427-13. 
9.  829-602. 

Find  the  missing  numbers  in  Exs.  10-1 7 : 
10.  683  -  *  =  32.  11.  891  -  *  =  20. 

12.  987-*  =  65.  13.  832-*  =  10. 

14.  775  -  *  =  700.  15.  698  -  *  =  125. 

16.  379  -  *  =  240.  17.  456  -  *  =  125. 

18.  If  a  man  earns  $125  in  January,  $202  in 
February,  and  $150  in  March,  how  much  does  he 
earn  in  the  three  months  ? 

19.  If  he  spends  $225  during  the  three  months, 
how  much  will  he  have  left  ? 

Make  problems  for  Exs.  20-31,  and  find  the 
answers : 

20.  $125 +  $230,  21.  $270 +  $106. 
22.  $175 +  $300.  23.  $450 +  $306. 
24.  $650  -  $loO.  25.  $775  -  $125. 
26.  $960 -$140.  27.  $395 -$162. 
28.  121  ft.  +  67  ft.  29.  421  ft.  +  75  ft. 
30.  62  yd.  +  104  yd.  31.  32  in.  +  107  in. 

Find  the  missing  numbers  in  Exs.  32-37 : 
32.  600  +  *  =  705.  33.  325  +  *  =  427. 

34.  322  +  *  =  344.  35.  275  +  *  =  286. 

36.  127  +  *  =  237.  37.  225  +  *  =  335. 


60 


PRIMARY   ARITHMETIC 


ORAL   EXERCISE 

1.  Point  to  the  pint,  quart,  and  gallon  measures. 

2.  Also  point 
to   the   quart, 
peck,  and  bushel 
measures. 

3.  Which  are 
used  for  liquids 
like  milk  and  oil? 

4.  Which  are 
used    for   any- 
thing dry  like 
grain  and  nuts? 

5.  Can  you  tell  how  many  quarts  make  a  gallon? 
A  quart  is  what  part  of  a  gallon? 

6.  Do  you  know  how  many  quarts  make  a  peck? 
How  many  pecks  make  a  bushel? 

7.  A  pint  is  what  part  of  a  quart?   of  a  gallon? 
A  quart  is  what  part  of  a  peck?     A  peck  is  what 
part  of  a  bushel  ? 

You  have  learned  that 

IN  MEASURING  LIQUIDS 

2  pints  (pt.)  =  1  quart  (qt.). 
4  quarts         =  1  gallon  (gal.). 

IN  DRY  MEASURE 


8  quarts  =  1  peck  (pk.)* 
4  pecks  =  1  bushel  (bu.). 


CAPACITY  61 

ORAL  EXERCISE 
BUYING  LIQUIDS 

1.  At  6  ct.  a  quart,  how  much  does  1  pt.  of  milk 
cost? 

2.  At  6  ct.  a  quart,  how  much  must  you  pay  for 
2qt.? 

3.  Oil  for  the  lamp  costs  14  ct.  a  gallon.     How 
much  will  2  qt.  cost? 

4.  If  a  gallon  of  oil  costs  12  ct..,  how  much  does 
1  qt.  cost? 

DRY  MEASURE 

5.  At  10  ct.   a  peck,  how  much  will  1  bu.   of 
potatoes  cost?     (Four  10's  are  how  many?) 

6.  How  many  quarts  in  a  peck?     1  qt.  is  what 
part  of  1  pk.  ? 

7.  How  many  pecks  in  a  bushel  ?    1  pk.  is  what 
part  of  1  bu.? 

8.  If  you  gather  4  qt.  of  nuts  on  one  day,  and 
3  qt.  the  next,  and  1  qt.  the  next,  how  many  pecks 
will  you  have? 

WRITTEN  EXERCISE 

1.  2  pt.  4-  3  pt.  +  5  pt.  =  how  many  pints?  how 
many  quarts? 

2.  2  times  4  qt.  =  how  many  quarts?  how  many 
gallons? 

3.  How  much  is  £  of  20  .bu.?  £of  40  gal.? 


62  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  Compasses  are  used  for  drawing  what  figures? 
In  the  picture  they  are  open  at  what  kinds  of  angles? 


Right  angle 


2.  See  if   you  can  find  in  the  room  two  lines 
which  make  a  right  angle. 

3.  When  do  the  hands  of  a  clock  make  a  right 
angle?  an  acute  angle?  an  obtuse  angle? 

Lines  drawn  like  these,  so  as  not  to  meet, 
however  long  we  make  them,  are  called  parallel  lines. 

4.  See  if  you  can  find  in  the  room  two  parallel 
lines. 

PAPER  FOLDING 

1.  Fold  a  2-in.  strip  of  paper  to  show  ^  of  it. 

2.  Fold  a  4-in.  strip  of  paper  to  show  |-  of  it ; 
|  of  it ;  |  of  it. 

3.  Cut  a  square  from  paper.     Fold  it  to  show  ^ 
of  one  of  its  angles ;  |  of  one  of  its  angles. 

4.  Fold  the  paper  so  as  to  show  2  parallel  lines. 
Fold  again  to  show  3  parallel  lines. 

5.  Fold   the   paper  to    make  an  obtuse  angle. 
Fold  again  to  make  |  of  this  angle.     This  is  what 
kind  of  angle? 


TIME  63 

ORAL  EXERCISE 

1.  What  time  is  it  now  by  the  clock? 

2.  How  many  minutes  does  it  take  the  minute 
hand  to  go  once  around? 

3.  What  month  is  this?    What  was  last  month? 
What  is  next  month?     Name  the  months  of  the 
year.     Name  the  days  of  the  week. 

4.  Do  you   know    how  many   seconds    make   1 
minute?    How  many  minutes  mak6  1  hour?    How 
many  hours  make  1  day  ?     How  many  days  make 
1  week? 

You  have  learned  that 

6O  seconds   (sec.)  =  1   minute   (min.). 
6O  minutes  =  1   hour   (hr.). 
24  hours  =  1  day  (da.). 
7  days  =  1  week  (\vk.). 

Four  months  have  30  days  each. 

Thirty  days  hath  September, 
April,  June,  and  November. 

February  has  28  days  except  in  leap  year,  when  it 
has  29  days.     The  other  months  have  31  days. 

WRITTEN   EXERCISE 

1.  5  da.  +  2  da.  =  how  many  days  ?  weeks  ? 

2.  2  times  30  sec.  =  how  many  seconds?  minutes? 

3.  40  sec. +  20  sec. —how  many  seconds?  minutes? 

4.  Write  the  day  of  the  week,  the  month,  and 
the  day  of  the  month,  thus  :  Thursday,  April  23. 


64 


PRIMARY   ARITHMETIC 


1 

square  inch 
1  sq.  in. 

lin. 


ORAL  EXERCISE 

1.  A  square  that  is  1  in.  on  a 
side  is  called  by  what  name? 

2.  If  the  area  of  such  a  square 
is    1    square    inch,   what   is   the 
area  of  an  oblong  1  in.  high  and 
2  in.  long  ?     1  in.  high  and  J  in. 
long? 

3.  The  picture  shows  some  piles  of  1-in.  blocks. 
How   many 

square  inches 
do  you  see  in 
A?  in  B? 
in  C? 

4.  What  is 
the    area    of 

an  oblong  2  in.  high  by  2  in.  wide  (see  A)?    of 
one  3  in.  by  2  in.?   of  one  4  in.  by  2  in.? 

5.  What  is  the  area  of  an  oblong  2  in.  by  5  in.? 

6.  What  do  you  mean  by  a  square  foot? 

We   write  sq.  in.  for  square  inch,   and  sq.  ft.  for 
square  foot. 

WRITTEN   EXERCISE 

1.  Copy  and  write  the  results : 

2x3  times  1  sq.  in.         2x5  times  1  sq.  ft. 
3  x  10  times  1  sq.  in.       1  x  25  times  1  sq.  ft. 

2.  Draw  a  picture  of  an  oblong  2  in.  by  5  in., 
using  \  in.  for  1  in.  in  your  drawing. 


SQUARE  MEASURE 


65 


ORAL  EXERCISE 

1.  This  strip  of  land  is  10  ft.  wide,  the  grass  on 
the  left  is  1  ft.  wide,  and  the  hedge  on  the  right  is 
2  ft.  wide.    How 

wide  is  the  garden  ? 

2.  These   chil- 
dren put  a  walk 
1  ft.  wide  through 
the  middle  of  the 
garden.      What 
width    was    left 
for     the     flower 
beds?   How  wide 
was  each  bed? 

3.  The  strip  was  80  ft.  long,  and  they  divided 
this  into  8  equal  parts.     How  long  was  each? 

4.  They  then  cut  each  part  into  2  equal  parts  for 
beds.     How  long  was  each  of  these  parts? 

5.  They  cut  1  ft.  from  the  length  of  each  bed 
for  cross  walks.     How  long  did  this  leave  each  bed? 

6.  The  beds  are  now  4  ft.  long  and  3  ft.  wide. 
How  many  square  feet  in  each? 

7.  Mabel  makes  a  violet  bed  10  in.  long  and  7  in. 
wide.     How  many  square  inches  does  it  contain? 

8.  How  many  inches  of  string  will  it  take  to  go 
around  Mabel's  violet  bed?     How  many  feet  will 
it  take  to  go  around  her  whole  bed,  which  is  4  ft. 
long  and  3  ft.  wide? 


66 


PRIMARY   ARITHMETIC 


COUNTING  BY  VARIOUS  NUMBERS 

ORAL  EXERCISE 

1.  If  there  are  5  peas  in  each  pod,  how  many  in 

2  pods? 

2.  How  many  in 

3  pods?   in  4  pods? 
in  5  pods? 

3.  Write  the   5's 
in  columns,  on  the 
blackboard,    to   ten 
5's.    (Five  such  are 
shown  here.)     Tell 
the  sums  rapidly,  be- 
ginning at  the  left. 

4.  Looking  at  the  columns  5 
in  Ex.  3,  5  is  |  of  what  num-                         5     5 
ber?  \  of  what  number?    10                    555 
is  twice  what  number?                       5     55     5 

5.  Look  again  at  the  col-       55555 
umns  and  give  some  exam- 
ples about  numbers  being  ^  or  ^  of  other  numbers. 

6.  Count  by  5's  from  5  to  100  and  back  again. 
Do  you  notice  how  this  pendulum  seems 

to  swing  from  0  to  5  and  back  each  time? 


The  basis  of  rapid  work  with  numbers  is  rapid 
counting.  Upon  it  rest  addition  and  the  multipli- 
cation tables,  with  their  inverses,  subtraction  and 
division. 


o 
10 

20 
30 


5 
15 

25 


9*8 


COUNTING  BY   FIVES 


67 


ORAL   EXERCISE 


1.  Count  the  cubes  by  columns,  thus:  5,  10,  15, 
and  so  on.  Count  them  by  horizontal  lines,  by 
10's,  and  see  if  you  have  the  same  number. 


2.  If  torpedoes  cost  5  ct.  a  package,  how  many 
packages  can  you  buy  for  20  ct.?     How  many  5's 
in  20? 

3.  Some  children  made   these   little  wigwams, 
using  a  piece  of  muslin  1  ft.  square  for  each.     How 
many  square  feet  were  used  for  all? 


4.  How  many  square  feet  would  be  needed  for 
4  times  as  many  wigwams? 

5.  If  the  muslin  costs  2  ct.  a  square  foot,  how 
much  will  the  5  sq.  ft.  used  for  the  wigwams  in 
the  picture  cost? 


68  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  Count   by  .5's   from   5  to  50.     Count  again, 
saying,  "  One  5  is  5,  two  5's  are  10,  three  5's  are 
15,"  and  so  on. 

2.  Count  in  this  way :  "  In  5  there  is  one  5,  in 
10  there  are  two  5's,  in  15  there  are  three  5's," 
and  so  on  to  50. 

3.  How  much  is  5  +  5  + 5?     3  +  3  +  3  +  3  +  3? 
How  many  are  three  5's?   five  3's? 

4.  Tell  the  value  of  each  of  the  following: 

1x5  5x1  6x5  5x6 

2x5  5x2  7x5  5x7 

3x5  5x3  8x5  5x8 

4x5  5x4  9x5  5x9 

5x5  5x5  10  x  5  5x10 

These  tables  and  the  tables  in  Ex.  6,  having  been  developed 
by  counting,  should  be  thoroughly  memorized,  and,  like  all  such 
tables,  be  made  the  subject  of  constant  rapid  review.  The  fives 
being  easiest  are  taken  first. 

5.  How  much  is  5  +  5  +  5  +  5?      4  +  4  +  4  +  4  +  4? 
4x5?      5x4?     How  many  5's  in  20?     How 
many  4's  in  20? 

6.  Tell  the  value  of  each  of  the  following: 
5-5          5-1  30-5        30-6 

10-5  10-2  35-5  35-7 

15-5  15-3  40-5  40-8 

20-5  20-4  45-5  45-9 

25  +  5  25-5  50  +  5  50+10 


COUNTING   BY   TWOS  69 


ORAL  EXERCISE 

1.  In  the  picture  how  many  groups  of  2  cubes 
each? 


2.  Count  the  cubes  by  2's,  thus :  2,  4,  6,  8,  10, 
to  20. 

3.  How  many  pairs  of  eyes  are  looking  at  me? 
How  many  eyes? 

4.  How  many  pairs  of  ears  are  listening  to  me? 
How  many  ears? 

5.  How  many  pairs  of  hands  are  on  the  desks? 
How  many  hands? 

6.  Write  on  the  blackboard  2 
and  add  columns  of  2's  as  far                        2     2 
as  ten  2's.     Here  are  5  such                 222 
columns.                                                2222 

7.  Look    at    the    columns.     22222 
2  is  J  of  what  number  ?     ^  of 

what  number?     ^  of  what  number? 

8.  How    many    2's  in  4?   in   8?   in  10?     How 
many  2-ct.  stamps  can  you  buy  for  10  ct.  ? 

9.  Count  by  2's,  beginning  with  1,  thus :  1,  3, 
5,  7,  9,  to  21. 

In  the  review  drills  this  should  be  carried  to  99. 

Just  as  |  of  4  means  4  -5-  2,  and  J  of  9  means  9-5-3, 
so  10  -H  5  may  be  written  ^  of  10, 12  -5-  6  may  be  written 
of  12,  and  so  on. 


70  PRIMARY    ARITHMETIC 

ORAL    EXERCISE 

1.  Count  by    2's  from  2  to  20.     Count  again, 
saying,  "  One  2  is  2,  two  2's  are  4,  three  2's  are  6," 
and  so  on. 

2.  Count  in  this  way  :  "  In  2  there  is  one  2,  in 
4  there  are  two  2's,  in  6  there  are  three  2's,"  and 
so  on  to  20. 

3.  How  much  is  2  +  2  +  2?     3  +  3?     Compare 
3x2  and  2x3.    How  many  2's  in  6?    How  many 
3's  in  6? 

4.  State  rapidly  the  value  of   each  of  the  fol- 
lowing : 

1x2  2x1  6x2  2x6 

2x2  2x2  7x2  2x7 

3x2  2x3  8x2  2x8 

4x2  2x4  9x2  2x9 

-5x2  2x5  10  x  2  2  x  10 

Memorize  the  tables  found  in  Exs.  4  and  5. 

5.  State  rapidly  the  value  of   each  of  the  fol- 
lowing : 


2-2 

2-1 

12-2 

12-6 

4-2 

4-2 

14-2 

14-7 

6*2 

6-3 

16-2 

16-8 

8-2 

8-4 

18-2 

18-9 

10-2 

10-5 

20-2 

20-10 

WRITTEN   EXERCISE 

Copy  Exs.  4  and  5  above  and  write  the  answers. 


COUNTING 


71 


ORAL  EXERCISE 

The   children  played  bean   bag   to-day.     Each   bag 
thrown  into  the  circle  counted  2.    Each  child  had  6  bags. 

1.  The  first. time  Rose  tried  she  threw  all  of  the 
bags  into  the  circle.     How  much  did  that  count? 

2.  The  second    time  she  threw  all  but  one  in, 
and  the  third  time  the  same.    What  was  her  score? 

3.  Tony  threw  in  5  the  first  time,  2  the  second, 
and  4  the  third.     What  was  his  score? 

4.  Donald  threw  in  4  the  first  time,  6  the  second, 
and  3  the  third.     What  was  his  score? 

5.  The  next  time  Rose  threw  in    5,  3,  and  4; 
Tony,  2,  6,  and  4 ;  Donald,  6,  6,  and  0.     Let  us 
write  their  scores  on  the  blackboard  and  see  who 
won. 


72  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  In  the  picture  how  many  groups  of  3  fire- 
crackers each?  How  many  firecrackers  in  2 
groups?  How  many  are  two  3's? 


2.  How   many  in  3  groups?     How    many  are 
three  3's?     How  many  are  four  3's?   five  3's? 

3.  Write   on   the    blackboard  „ 
columns  of  3's  as  far  as  ten  3's.                         ~     o 
Here    are    five    such    columns.                   o     o     o 
Add  those  on  the  board.                          o     o     o     o 

4.  Count  by  3's,  thus:  3,  6,  9,      33333 
12,  and  so  on  to  30. 

5.  From  these  columns  you  see  that  3  is  ^  of 
what  number  ?  ^  of  what  number  ?  £  of  what  num- 
ber ?  I  of  what  number  ? 

6.  How  many  3's  do  you  see  in  9?   in  a  dozen? 

7.  How  many  feet  in  1  yd.?   in  3  yd.?  in  5  yd.? 

8.  If  each  of  5  boys  has  3  ct.,  how  much  have 
they  all? 

9.  If  each  of  7  boys  has  3  marbles,  how  many 
have  they  all? 

10.  At  3  ct.  each,  how  many  pencils  can  be  bought 
for9ct.?   15  ct.?   21  ct.? 

In  review  drills,  count  by  3's  beginning  with  1. 


TABLES   OF    THREES  73 

ORAL   EXERCISE 

1.  Count  by  3's  from  3  to  30.    Count  again,  say- 
ing, "  One  3  is  3,  two  3's  are  6,"  and  so  on. 

2.  Count  in  this  way :  "  In  3  there  is  one  3,  in 
6  there  are  two  3's,  in  9  there  are  three  3's,"  and 
so  on  to  30. 

3.  State  rapidly  and  memorize  the  value  of  each : 


1x3       3x1 

6x3 

3x6 

2x3       3x2 

7x3 

3x7 

3x3        3x3 

8x3 

3x8 

4x3        3x4 

9x3 

3x9 

5x3       3x5 

10  x  3 

3  x  10 

4.  State  rapidly  and 

memorize  the 

value  of  each 

3-3         3-1 

18  -  3 

18-    6 

.    6+3        6-2 

21-3 

21-    7 

9-3         9-3 

24-3 

24-8 

12-3       12-4 

27-3 

27-9 

15  -  3      15-5 

30-3 

30-10 

5.  State  rapidly  these  sums  and  differences: 
3  +  0        3-3  3  +  10       13-3 

3  +  2         5-3  3  +  12       15-3 

3  +  4         7-3  3  +  84       87-3 

3  +  6         9-3  3+7       10-3 

3  +  9       12-3  3  +  19      22-3 

WRITTEN   EXERCISE 

Copy  Exs.  3  and  4  above  and  write  the  answers. 


74  PRIMARY    ARITHMETIC 

ORAL   EXERCISE 

1.  In  the  picture  how  many  columns  of  4  squares 
each?     How  many  squares  in  2  columns?     in  3 

columns  ?  How  many 
are  two  4's?  three 
4's? 

2.  Write  on  the 
blackboard  and  add 
the  columns  of  4's  as  far  as  ten  4's.  (See  the 
columns  of  3's  on  page  66.) 

3.  Count  by  4's,  thus :  4,  8,  12,  16,  and  so  on 
to  40. 

4.  From  the  columns  on  the  blackboard  you  see 
that  4  is  ^  of  what  number?     £,  ^,  |,  £  of  what 
numbers  ? 

5.  How  many  4's  do  you  see  in  8?   in  12?   in 
16?    in  32? 

6.  If  each  of  5  boys  has  4  ct.,  how  many  cents 
have  they  all? 

7.  How  many  25-ct.  pieces  in  $1?    How  many 
in  $4? 

8.  How  many  quarts  in  1  gal.  ?     How  many  in 
5  gal.?  in  7  gal.? 

9.  If  4  ct.  pays  for  1  yd.  of  ribbon,  how  many 
yards  can  be  bought  for  20  ct.?   for  36  ct.? 

10.  If  4  ct.  pays  for  1  yd.  of  ribbon,  what  is  the 
cost  of  5  yd.?  of  6  yd.?  of  9  yd.?  of  8  yd.?  of 
10yd.? 


TABLES   OF   FOURS  75 

ORAL  EXERCISE 

1.  Count  by  4's  from    4  to  40.     Count  again, 
saying,  "  One  4  is  4,  two  4's  are  8,"  and  so  on. 

2.  Count  in  this  way  :  "  In  4  there  is  one  4,  in 
8  there  are  two  4's,  in  12  there  are  three  4's,"  and 
so  on  to  40. 

3.  State  rapidly  and  memorize  the  value  of  each  : 
1x4         4x1  6x4         4x6 


2x4         4x2 
3x4         4x3 
4x4         4x4 
5x4        4x5 

4.  State  rapidly  and 
4-4          4-1 
8-4         8-2 
12-4        12-3 
16-4        16-4 
20-4       20-5 

7x4 
8x4 
9x4 
10  x  4 

memorize  the 
24-4 
28-4 
32-4 
36-4 
40-4 

4x7 
4x8 
4x9 
4  xlO 

value  of  each: 
24-6 
28-7 
32-8 
36-9 
40-10 

Teachers  should  give  abundant  drill  on  all  such  tables,  asking 
for  products  and  quotients  in  irregular  order. 

5.  State  rapidly  these  sums  and  differences: 
4  +  2     6-4     6-2         4+7     11-4     11  --7 
4  +  4     8-4     8-4          4+9      13-4      13-9 
4  +  5     9-4     9-5         4+10     14-4      14-10 

WRITTEN   EXERCISE 

Copy  Exs.  3  and  4  above  and  write  the  answers. 


76 


PRIMARY  ARITHMETIC 


REVIEW   OF   THE   TABLES 

You  have  now  learned  how  to  add  any  two  numbers 
of  one  figure  each.  There  are  45  ways  in  which  you 
can  put  two  such  numbers  together,  and  you  know  them. 

23456789 

1  +  1     1  +  2    1+3    1+4    1  +  5    1  +  6    1  +  7    1  +  8 

2  +  2    2  +  3    2  +  4    2  +  5    2  +  6    2  +  7 

3  +  3    3  +  4    3  +  5    3  +  6 

4  +  4    4  +  5 

10         11         12        13        14        15        16        17        18 

1  +  9  2  +  9  3  +  9  4  +  9  5  +  9    6  +  9    7  +  9    8  +  9    9  +  9 

2  +  8  3  +  8  4  +  8  5  +  8  6  +  8    7  +  8    8  +  8 

3  +  7  4  +  7  5  +  7  6  +  7  7  +  7 

4  +  6  5  +  6  6  +  6 

5  +  5 

The  following  table  also  shows  the  sum  of  the  left- 
hand  number  and  top  number. 


1+ 

1  — 

2 

2  = 

3  = 
4 

4  = 

5 

5  = 
6 

6  = 

7 

1  = 
8 

8  = 
9 

9  = 
10 

3 

2  + 

3 

4 

5 

6 

7 

8 

9 

10 

11 

3  + 

4  + 

4 

5 

6 

7 

8 

9 
10 

10 

11 

12 

'5 

6 

7 

8 

9 

11 

12 

13 

5  + 

6 

7 

8 

9 

10 

11 

12 

13 

14 

6  + 

7 

8 

9 

10 

11 

12 

13 

14 

15 

7  + 

8 

9 

10 

11 

12 

13 

14 

15 

16 

8  + 

9 

10 

11 

12 

13 

14 

15 

16 

17 

9  + 

10 

11 

12 

13 

14 

15 

16 

17 

18 

MULTIPLICATION    AND   DIVISION   TABLES      77 

You  have  also  learned  how  to  multiply  and  divide 
certain  numbers. 

lx2or2xl-2  2+-2-  1  2  -  1  -  2 

2x2                    -4  4-2-2  4-2-2 

3x2  or  2x3=    6  6-2-3  6-3-2 

4x2  or  2x4-8  8-2-4  8-4-2 

5x2  or  2x5- 10  10-2-5  10-5-2 

6x2  or  2x6- 12  12-2-6  12-6-2 

7x2  or  2x7- 14  14-2-7  14-7-2 

8x2  or  2x8- 16  16-2-8  16-8-2 

9  x  2  or  2  x    9  -  18  18-2-9  18-9-2 

10  x  2  or  2  x  10 -20  20-2-10  20-10-2 

1x3  or  3x1-3  3-3-1  3-1-3 

2x3or3x2-6  6-3-2  6-2-3 

3x3                   -    9  9-3- 3  9- 3-3 

4x3  or  3x4- 12  12-3-4  12-4-3 

5x3  or  3x5- 15  15-3-5  15-5-3 

6x3  or  3x6- 18  18 -3=  6  18-6-3 

7  x  3  or  3  x    7-21  21-3-7  21-7-3 

8  x  3  or  3  x    8-24  24-3-  8  24-  8-3 
9x3  or  3x9- 27  27-3-9  27-9-3 

10  x  3  or  3  x  10 -30          30-3-10          30-10-3 

The  multiplication  tables  thus  far  learned,  with  the  accom- 
panying results  of  division,  are  here  given  for  the  convenience 
of  the  teacher  in  arranging  reviews,  and  that  the  pupils  may  be 
assisted  in  visualizing  results.  For  oral  work  the  teacher  should 
not  usually  ask  for  products  or  quotients  in  the  order  given 
by  the  tables. 


78  PRIMARY   ARITHMETIC 


Ix4or4x   1  =   4 

4-4  =  1 

4-  1=4 

2x4or4x    2  =    8 

8-4  =  2 

8-s-  2  =  4 

3x4or4x   3  =  12 

12-s-4  =  3 

12-1-  3=4 

4x4                   =16 

16-4  =  4 

16-  4  =  4 

5  x  4  or  4  x   5  =  20 

20-4  =  5 

20-  5  =  4 

6  X  4  or  4  X    6  =  24 

24-4  =  6 

24-  6  =  4 

7x4or4x   7  =  28 

28-4  =  7 

28-  7  =  4 

8x4or4x   8  =  32 

32-4  =  8 

32-  8  =  4 

9x4or4x   9  =  36 

36-s-4=  9 

36-  9  =  4 

10  x  4  or  4  x  10  =  40 

40-4=10 

40-10=4 

Ix5or5x   1=   5 

5-5=  1 

5-5-  1  =  5 

2x5or5x   2  =  10 

10-5-5=  2 

10-  2  =  5 

3x5or5x   3  =  15 

15-5=  3 

15-  3  =  5 

4x5  or  5x4  =  20 

20-5-5=  4 

20-5-  4  =  5 

5x5                   =25 

25-5=  5 

25-s-  5  =  5 

6x5or5x   6  =  30 

30-5=  6 

30-  6  =  5 

7x5or5x   7  =  35 

35-5=  7 

35-  7  =  5 

8x5or5x   8  =  40 

40-5=  8 

40-  8  =  5 

9x5or5x   9  =  45 

45-5=  9 

45-  9  =  5 

10  x  5  or  5  X  10  =  50 

50-5=10 

50+10  =  5 

WRITTEN   EXERCISE 

1.  Make    15  dots  so  as  to  show  that  there  are 
three  5's  in  15,  and  five  3's  in  15. 

2.  Draw  6  squares  so  as  to  show  that  2  x  3  is 
the  same  number  as  3  x  2. 

3.  Make  12  dots  so  as  to  show  that  3  x  4  is  the 
same  number  as  4  x  3. 

4.  Make  10    dots  so  as  to  show  that  there  are 
two  5's  in  10,  and  five  2's  in  10. 


ADDITION 


79 


ADDITION 

We  see  by  this  example  that  we  may  add  each  column 
separately  and  then  add  the  sums. 

Learn  thread  the  columns  like  words.     34 
When  you  see  7+4,  think  simply  11. 

To  be  sure  that  your  answer  is  right, 
to  check  it  as  we  say,  add  in  the  other 
direction,  that  is,  from  the  top  down, 
if  you  first  added  upwards. 


47 

11  sum  of  units 
7       "     "  tens 
81  total  sum 


WRITTEN  EXERCISE 


Add  the  following : 


1. 

27 

2.  26 

3.  39 

4.  56 

5.  35 

38 

49 

48 

18 

45 

6. 

12 

7.  33 

8.  27 

9.  42 

10.  57 

23 

28 

13 

28 

6 

46 

31 

36 

13 

20 

11. 

31 

12.  22 

13.  80 

14.  34 

15.  63 

41 

30 

90 

23 

41 

22 

63 

27 

40 

32 

34 

74 

42 

50 

70 

16. 

11 

17.  60 

18.  76 

19.  43 

20.  30 

21 

22 

20 

21 

33 

32 

35 

31 

32 

23 

41 

40 

40 

41 

13 

70 

21 

21 

11 

30 

80  PRIMARY    ARITHMETIC 

ORAL  EXERCISE 

State  the  sums  rapidly.  Do  not  repeat  the  num- 
bers to  be  added. 

l.  7         2.  27         3.  27         4.  27      *  5.  37 
4  J  14  24  34 

In  oral  work,  children  should  add  27  to  14  by  thinking 
27  +  4  =  31,  31  +  10  =  41,  or  27  +  10  =  37,  37  +  4  =  41.  Much 
oral  work  of  this  kind  should  be  given.  Explanations  like  the 
following  should  be  placed  on  the  blackboard. 

You  have  now  found  that  you  need  not  stop  to  write 
the  sum  of  each  column,  as  on  page  79. 

You  may  think  this:  But  write  only  this: 
35  35 

28  28 

13  sum  of  units  63 

5       "     "  tens 
63  sum 

In  this  example  you  look  at  8  and  5,  and  think  13. 
Then  you  write  the  3  in  units'  place  and  add  the  1  ten 
to  the  tens'  column.  The  tens  are  then  1  +  2  +  3  =  6. 

WRITTEN  EXERCISE 


Add  the  following: 

1. 

42 

2. 

73 

3. 

29 

4.  36 

5.  48 

38 

18 

39 

27 

29 

6. 

256 

7. 

329 

8. 

635 

9.  725 

10.  807 

127 

438 

125 

106 

153 

ADDITION  81 

ORAL  EXERCISE 

1,  352  2.  300  +  50  +  2  3.  300  +  50  +  6  4.  356 

224    200  +  20  +  4    200  +  20  +  4    224 

These  examples  should  be  written  on  the  blackboard,  the  chil- 
dren reciting  orally.  See  the  note  on  page  80. 

As  with  numbers  of  two  figures, 

You  may  think  this:  But  write  only  this: 

384  384 

257  257 

11  sum  of  units  641 

13       "     "  tens 

5         "     "  hundreds 

641  sum 

You  look  at  7  and  4,  and  think  11.  Then  you  write 
the  1  in  units'  place,  and  add  the  1  ten  to  the  tens' 
column.  The  tens  are  then  1  +  5  +  8  =  14.  Then  you 
write  the  4  in  tens'  place  and  add  the  1  to  the  hundreds' 
column.  The  hundreds  are  then  1  +  2  +  3=6. 


WRITTEN 

EXERCISE 

Add  the  following  : 

1.  122 

2.    125 

3.  155 

347 

348 

348 

5.  298  ft. 

6.  400 

7.  201 

107 

102 

507 

206 

70 

92 

101 

99 

61 

4.  265 
348 

8.  |374 

385 

62 

101 


82  PRIMARY   ARITHMETIC 

WRITTEN  EXERCISE 

Add  in  Exs.  1-10: 

1.  132  2.  209  3  122  4.  302  5.  122 

227  108  231  47  129 

342  301  327  509  324 

135  250  152  51  150 


6. 

223 

7.  102 

8.  200 

9.  350 

10.  230 

47 

75 

37 

107 

30 

142 

327 

47 

150 

40 

31 

22 

122 

103 

•  9 

21 

401 

31 

200 

109 

11.  If  Fred  picks  225  apples,  Frank  235,  and  Rob 
236,  how  many  do  they  all  pick? 

Make  problems  for  Exs.  12-26,  and  find  the 
ansivers : 

12.  235+475+60.    13.  125+75  +  300. 
14.  240  +  40  +  608.    15.  325  +  25  +  250. 

16.  $175 +  $50 +  $75.  17.  $350 +  $350 +  $200. 
18.  $250 +  $350 +  $50.  19.  $225 +  $225 +$250. 

20.  325  ft.  +  40  ft.  +  75  ft. 

21.  600  ft.  +  82  ft.  +  79  ft. 

22.  427  yd.  +  23  yd.  +  50  yd. 

23.  328  yd.  +  37  yd.  +  39  yd. 

24.  4  Ib.  +  9  Ib.  +  73  Ib.  +  68  Ib. 

25.  56  Ib.  +  72  Ib.  +  68  Ib.  +  49  Ib. 

26.  63  Ib.  +  59  Ib.  +  67  Ib.  +  58  Ib. 


ADDITION  83 


WRITTEN  EXERCISE 


Add: 
1.  223   2.  121   3.  102   4.  320   5.  221 
37     306     302      25     322 
123     250     55      75      37 
203     127     23      30      42 
61      32      31     400      13 

6. 

311     121     232     105 

201 

92   7.  82   8.  22   9.  23  10.  42 

11.  34 

23    31    33    35     62 

60 

42    22    23    42     13 

75 

27    19    44    52     19 

25 

13    32    25    63     52 

12 

11    13    81    11     31 

32 

12. 

325  +  144.  13.  347  +  279.  14.  352 

+  179. 

15. 

237  +  473.  16.  395  +  295.  17.  406 

+  499. 

18. 

328  +  376.  19.  245  +  259.  20.  307 

+  498. 

21. 

62  +  98  +  179.     22.  35  +  49  +  675 

B 

23. 

28  +  43  +  596.     24.  87  +  50  +  509 

t 

25. 

75  +  75  +  175.     26.  86  +  98  +  344 

27. 

$675  +  $87  +  |21.  28.  |243  +  $95  +  |327. 
29.  $86  +  $9  +  $772. 
30.  46  in.  +  98  in.  +  21  in. 

31.  28  qt.  +  39  qt.  +  62  qt. 
32.  221  ft.  +  87  ft.  .+  65  ft. 

33.  306  ft.  +  85  ft.  +  32  ft. 

34.  227  ft.  +  49  ft.  +  353  ft. 

.  35.  43  yd.  +  37  yd.  +  21  yd. 

84  PRIMARY   ARITHMETIC 

SUBTBACTION 

ORAL   EXERCISE 


1. 

8 

2. 

18 

3. 

48 

4.  357 

5. 

357 

2 

2 

12 

12 

123 

6. 

98 

7. 

69 

8. 

75 

9.  225 

10. 

475 

73 

42 

25 

25 

150 

The  above  are  types  of  examples  to  be  written  on  the  black- 
board, the  children  reciting  orally. 

11.  What  number  must  be  added  to  15  to  make 
20  ?     to  15  to  make  25  ?     to  75  to  make  100  ? 

12.  Which  is  larger,  the  sum  of  two  numbers  or 
one  of  the  numbers  ?     How  much  larger  ?     Think 
of  4  +  5  =  9. 

In  subtracting  47  -  23  =  24, 

47  is  called  the  minuend, 

23  "      "        "    subtrahend, 

24  "      "        "    difference  or  remainder. 

Teachers  will  see  the  advantage  of  following  the  method  of 
subtraction  in  use  in  the  other  classes  in  the  school,  so  as  to  avoid 
confusing  children.  Either  of  the  following  is  satisfactory,  the 
first  being  the  quicker. 

1.  3  and  4  are  7  ;  2  and  2  are  4.     Write  the  24. 

2.  3  from  7  are  4 ;  2  from  4  are  2.     Write  the  24. 

The  pupils  should  be  required  to  check  results  by  adding  the 
difference  and  the  subtrahend. 

It  is  often  necessary  in  a  text-book  to  present  a  considerable 
amount  of  abstract  work  on  consecutive  pages.  Teachers,  how- 
ever, should  daily  give  practical  problems  from  the  children* s  life 
of  the  types  found  throughout  this  book. 


SUBTRACTION  85 

ORAL  EXERCISE 

1.  400  +  110  +  13  2.  600  +  130  +  11 

100+    50+4  200+    50+2 

3.  300  +  120  +  15  4.  800  +  150  +  10 

100+    30+9  600+    80+5 

See  the  note  on  page  80  as  to  this  work. 

You  have  here  subtracted  numbers  of  3  figures  by 
separating  them.     In  subtracting  154  from  523, 

You  may  think  this:          But  write  only  this: 

400  +  110  +  13  523 

100+    50+4  154 

300+    60+9  369 

The  pupil  may  think  either 

1.  4  and  9  are  13 ;  5  (tens)  and  6  are  11  (or  6  and  6  are  12) ; 
1  and  3  are  4  (or  2  and  3  are  5).     Write  369. 

2.  Or,  4  from  13,  9  ;  5  (tens)  from  11,6;    1  from  4,  3. 

• 

WRITTEN  EXERCISE 

Subtract,  separating  only  in  Exs.  1  and  2: 

1.  236  =  200  +  20  +  16          2.  431  =  400  +  20  +  11 
127  =  100  +  20+  7  229  =  200  +  20+   9 

3.  $346  4.  487  ft.  5.  346  min. 

209  192  157 

6.  326-134.         7.  420-140.         8.  342-168. 
9.  900-206.       10.  342-127.       11.  680-469. 


86  PRIMARY    ARITHMETIC 

WRITTEN   EXERCISE 

1.243-26.         2.327-63.         3.492-96. 

4.627-29.         5.346-66.         6.821-32. 

7.593-287.  8.609-590.  9.341-143. 
10.  623-129.  11.  648-249.  12.  273-164. 
13.592-293.  14.407-328.  15.621-269. 
16.821-327.  17.360-172.  18.731-235. 
19.  732-648.  20.  500-419.  21.  800-635. 
22.  $204 -$68.  23.  $325 -$75.  24.  $750 -$175. 
25.  300  ft.  -  67  ft.  26.  225  ft.  -  70  ft. 

27.  340  yd.  -  85  yd.  28.  285  yd.  -  98  yd. 

29.  307  min.  -  39  min.  30.  250  ft.  -  198  ft. 

31.  If  Ned  had  850  ft.  of  kite  string  and  lost 
69  ft.  in  a  tree,  bow  many  feet  had  he  left? 

Make  problems  for  Exs.  32-43,  and  find  the 
answers : 

32.  700       33.  820      34.  650      35.  295      36.  745 
'  95  75  80  96  37 

37.  925       38.  871      39.  482      40.  520      41.  630 
367  293  193  175  182 

42.  $825  -  $268.  43.  $342  -  $175. 

First  add  the  numbers  in  the  parenthesis;  then 
subtract  : 

44.  635  -  (75  +  132).  45.  825  -  (67  +  139). 
46.  462  -  (73  +  246).  47.  521  -  (25  +  247). 
48.  762  -  (32  +  167).  49.  384  -  (48  +  121). 


MULTIPLICATION  87 

MULTIPLICATION 

ORAL  EXERCISE 

1.  10  +  2  2.  10  +  8  3.  20  +  4 

5  2  3 

#  _l-  #  =  #  #_!_#  —  %  #  _j_  #  =  # 

See  the  note  on  page  80  as  to  this  work. 
In  multiplying  23  by  3, 

23  is  called  the  multiplicand, 
3  "       "        "    multiplier, 

69  "       "       "   product. 

You  have  multiplied  by  separating  the  multiplicand 
into  parts.  You  need  not  take  the  time  to  do  this. 

You  may  think  this:       Or  this:          But  write  only  this: 
20+7  27  27 

3  J*  _3 

60  +  21  =  81        21  product  of  units         81 
6  "        "  tens 

81  total  product 

You  should  think  3  times  7  =  21.  (Write  the  1  in 
units'  place.)  3  times  2  (tens)  =  6  (tens),  and  6  (tens)  +  2 
(tens)  =  8  tens.  (Write  the  8  in  tens'  place.) 

WRITTEN  EXERCISE 

Multiply: 

1.  23  by  3.  2.  23  by  4.  3.  25  by  2.  4.  25  by  3. 

5.  45  by  2.  6.  17  by  3.  7.  13  by  3.  8.  38  by  3. 

9.  19  by  3.  10.  18  by  3.  11.  21  by  4.  12.  37  by  3. 

13.  46  by  2.  14.  36  by  2.  15.  16  by  3.  16.  28  by  2. 


J  PRIMARY   ARITHMETIC 

WRITTEN   EXERCISE 

Multiply  in  Exs.  1-30 : 


1. 

26 

2. 

37 

3. 

48 

4. 

39 

5. 

47 

_2 

_2 

_2 

2 

_2 

6. 

15 

7. 

24 

8. 

26 

9. 

29 

10. 

28 

_3 

_3 

3- 

_3 

3 

11. 

17 

12. 

19 

13. 

25 

14. 

33 

15. 

36 

_4 

_4 

_4 

4 

4 

16. 

15 

17. 

17 

18. 

26 

19. 

32 

20. 

37 

_5 

_5 

_5 

_5 

_5 

21. 

45 

22. 

52 

23. 

68 

24. 

73 

25. 

82 

_3 

_3 

_4 

4 

_5 

26. 

91 

27. 

89 

28. 

93 

29. 

95 

30. 

96 

2 

2 

3 

4 

5 

31.  How  many  wings  have  35  robins? 

32.  What  will  18  oranges  cost  at  5  ct.  each? 

Make  problems  for  Exs.  33-4%,  and  find  the 
answers : 

33.  3  times  44.  34.  4  times  33. 
35.  5  times  62.  36.  2  times  $75. 
37.  3  times  $55.  38.  4  times  $32. 
39.  5  times  71  ft.  40.  4  times  25  ct. 
41.  4  times  41  Ib.  42.  3  times  33  yd. 


MULTIPLICATION  89 

ORAL  EXERCISE 

1.  What  is  the  value  of  the  following  ? 
3+3  2+2+2  2x3      3x2 
4+4+4     3+3+3+3     3x4      4x3 

Two  3's  equal  how  many  2's  ?     Three  4's  equal 
how  many  3's  ? 

2.  How  many  dots  are  there  in  each  horizontal 
row?      How   many    rows    are   there?     •  •  •  •  • 
Then  how  many  dots  are  there  in  all?     •  •  •  •  • 

3.  How  many  dots  in  each  column?     •  •  •  •  • 
How  many  columns  are  there?     Then  how  many 
dots  are  there    in  all?     What  does  this  tell  you 
about  the  values  of  3  x  5  and  5x3? 

4.  Instead  of   multiplying  2   by   15,  you   may 
multiply  15  by  what  number?     Instead  of  multi- 
plying $3  by  12,  you  may  multiply  $12  by  what 
number? 

5.  If  one  pair  of  shoes  costs  $2,  how  much  will 
15  pairs  cost?    You  can  get  the  result  by  multi- 
plying $15  by  what  number? 

WRITTEN   EXERCISE 

1.  At  $2  each,  how  much  will  17  books  cost? 

2.  At  $4  each,  how  much  will  24  tricycles  cost? 

3.  If  one  hat  costs  $  3,  how  much  will  14  such 
hats  cost? 

4.  If  one  sled  costs  75  ct.,  how  many  cents  must 
be  paid  for  two  such  sleds  ? 


90  PRIMARY    ARITHMETIC 

DIVISION 
ORAL  EXERCISE 

State  rapidly  the  results: 
1.  3x4,        12-3.  2.  3x  5,         15-3. 

3.  2x  7,        14  +  2.  4.  2x  9,         18-2. 

5.2x60,    120  +  2.  6.3x70,     210  +  3. 

To  show  that  we  divide  8  by  2  we  may  write : 
i  of  8=4  8-^2  =  4 


7.  3)30+3      3)30+6         8.  2)40+4 

9.  2)80+4      3)90+6       10.  2)120+6      3)120+9 

See  the  notes  on  pages  80  and  81. 

In  21  -f-3  =  7,  21,  the  number  divided,  is  called  the 
dividend;  3,  the  number  by  which  we  divide,  is  called 
the  divisor;  7,  the  result,  is  called  the  quotient. 

You  may  think  this:  But  write  only  this: 

3)30  +  6  3)36 

10  +  2  =  12  12 

WRITTEN  EXERCISE 

1.  63-8-3.  2.  48-4.  3.  88-s-S. 

4.  68-8-2.  5.  96-3.  6.  55-5. 

7.  248-2.  8.  464-2.  9.  844-4. 

10.  448-4.  11.  550-5.  12.  505-5. 

13.  639-3.  14.  309-3.  15.  966-3. 

16.  Jof  426.  17.  I  of  693.  18.  |  of  448. 

19.  |  of  800.  20.  |  of  500.  21.  |  of  20;  of  200. 


FRACTIONS  91 

FRACTIONS 
ORAL  EXERCISE 

1.  Using  real  cubes  or  this  picture,  point  to  the 
prism  made  up  of  5  blocks,  ^  of  5  blocks,  4 
blocks,  ^  of  4  blocks,  ^  of  4  blocks,  3 
blocks,  ^  of  3  blocks,  ^  of  2  blocks. 
2.  Show  by  the  blocks  that  ^  of 
4=  twice  ^  of  4.     If  you  have 
the   real  cubes,  pile    6  of 
IF    them  and  show  that  ^  of 
6-3  times  i  of  6. 

Cubes  of  this  kind  are  commonly  found  in  schools.  The 
above  is  suggestive  of  work  with  various  fractions,  the  arrange- 
ment in  steps  being  particularly  advantageous. 

DRAWING  EXERCISE 

1.  Draw  a  line  1  in.  long.     Mark  off  |  in.  on 
this  line. 

2.  Draw  a  line  1^  in.  long.    Divide  it  into  three 
equal  parts.     Write  over  each  part  its  length. 

3.  Draw  a  line  3  in.  long.    Divide  it  into  6  equal 
parts.     Show  from  this,  by  making  ^  of  the  line 
heavier,  that  ^  =  twice  £. 

4.  Draw  another  line  3  in.  long.    Divide  it  so  as 
to  show  that  J  =  3  times  ^. 

5.  Draw  an  oblong  8  in.  long  and  1  in.  high, 
separating  it  into   1-in.   squares.     Then  ^  =  how 
many  eighths  ?    -J  =  how  many  eighths  ? 


92  PRIMARY    ARITHMETIC 


ORAL  EXERCISE 

1.  Some  children  in  school  made  these  baskets 
out  of  raffia.     The  raffia  for  the  3  baskets  cost 
12  ct.     What  was  the  average  cost  of  each? 

2.  If  they  sold  each  basket  for  10  ct.  at  a  school 
fair,  what  was  the  average  gain  on  each?    What 
was  the  gain  on  the  three? 

3.  Of  these  three  baskets  the  largest  holds  1  qt. 
and   the  smallest  1  pt.     The  third  holds  half  as 
much  as  the  other  two  together.     How  much  does 
the  third  hold? 

4.  The   children  made  some  table  mats  out  of 
reeds.     They  paid  6  ct.  for  enough   reeds  for  a 
dozen  mats.     How  much  did  the  reeds  cost  for 
2  mats?  for  1  mat? 

WRITTEN  EXERCISE 

1.  John  made  2  small  baskets  in  3  hr.     How 
many  minutes  did  it  take  him  ? 

2.  At  that  rate,  how  long  would  it  take  him  to 
make  1  such  basket? 


ROMAN   NUMERALS  93 

ROMAN   NUMERALS 

ORAL   EXERCISE 

1.  Read  these  numbers  which  are  found  on  the 
clock  face : 

in,  ix,  xn,  i?  vn,  iv,  xi?  v. 

2.  Tell  the  time  when  the  minute  hand  points  to 
XII  and  the  hour  hand  to  IX;  to  XI;  to  II;  to  X; 
to  XII. 

The   Roman  numerals  are  also  used  for  numbering 
the  chapters  of  books. 

Ito  5:  I,  II,  III,  IV,  V. 

11  to  15:  XI,  XII,  XIII,  XIV,  XV. 

6  to  10:  VI,  VII,  VIII,  IX,  X. 

16  to  W:  XVI,  XVII,  XVIII,  XIX,  XX. 

3.  When  you  come  to  Chapter  XIV  in  a  book, 
how  many  chapters  have  you  read? 

4.  When   you  have    finished  Chapter  IX  of  a 
book,  and  the  last  chapter  is  XV,  how  many  chap- 
ters have  you  still  to  read? 

WRITTEN  EXERCISE 

1.  Write  in  Roman  numerals:  20,  12,  7,  6,  18, 
16,  19,  15. 

2.  Write  in  common  (Arabic)  numerals:  XI,  IX, 
IV,  VI,  XIX,  XIV,  XVII. 

3.  Write  your  age  in  Roman  numerals. 


CHAPTER   III 

I.    NUMBERS  TO  10,000 
READING  AND  WRITING  NUMBERS 


2000  +300  +40  +  2 

ORAL   EXERCISE 

1.  Count  by  1000's  from  1000  to  10,000. 

2.  How  many  splints  are  there  in  the  picture? 
Write  the  number  on  the  blackboard. 

3.  Read  the  numbers : 

27   270   2700   271   2710   2713 
35   350   3500   356   3560   3567 


WRITTEN  EXERCISE 

1.  Write  the  numbers : 

Two  thousand  three  hundred  forty-five 
Seven  thousand  eight  hundred  ninety 
Six  thousand  seven  hundred  eighty-nine 

2.  Write  in  words :  2143,  9009,  9876. 

94 


READING  NUMBERS  95 

ORAL   EXERCISE 

Read  aloud: 

1.  Columbus  discovered  America  in  1492.    George 
Washington  was  born  in  1732.     Henry  Hudson 
discovered  the  Hudson  River  in  1609.     The  Pil- 
grims landed  at  Plymouth  in  1620.     Boston  was 
founded  in  1630.     The  first  American  newspaper 
was  printed  in  Boston  in  1704. 

2.  The  Declaration  of  Independence  was  signed 
in  1776.    George  Washington  became  President  in 
1789.    The  first  passenger  railroad  in  America  was 
begun  in  1828.    The  great  Chicago  fire  was  in  1871 . 
Our  war  with  Spain  began  in  1898. 

You  have  learned  to  write  the  Roman  numerals  to 
XX,    twenty.      Although   not   much   used   for   larger 
numbers,  they  are  easily  written. 
From  21  to  30:    XXI,  XXII,  XXIII,  XXIV,  XXV, 

XXVI,  XXVII,  XXVIII,  XXIX,  XXX.    . 
From  31  to  40:  XXXI,  XXXII,  and  so  on  to  XXXIX, 

XL. 

From  41  to  50:  XLI,  XLII,  and  so  on  to  XLIX,  L. 
From  51  to  60 :  LI,  LII,  and  so  on  to  LIX,  LX. 

60  =  LX,   70-LXX,  80  =  LXXX,  90  =  XC. 
From  91  to  100:  XCI,  XCII,  XCIII,  XCIV,  and  so  on 

to  XCIX,  C. 

WRITTEN   EXERCISE 

1.  Write  in  Roman :  4,  42,  73,  75,  79,  84,  89. 

2.  Write  in  Arabic:  XXXIX,  XLIV,  LXXIX, 
LXXXVIII. 


96 


PRIMARY   ARITHMETIC 


MEASURES 
ORAL  EXERCISE 

1.  These  children  are  playing  store.     Jack  buys 

20  ct.  worth  of 
candy  and  gives 
a  quarter  of  a 
dollar.  How  much 
change  is  due  ? 

2.  Fanny  buys 
10   ct.  worth  of 
bananas  at  2  for 
a   nickel.      How 
many     bananas 
does  she  buy? 

3.  The    dealer 
says  that  oranges 

are  sold  at  3  for  a  dime.    How  much  will  half  a 
dozen  oranges  cost  ? 

We  write       $12.50  for    12  dollars  and  50  cents, 
$175.05  for  175  dollars  and    5  cents. 

That  is,  write  first  the  dollar  sign  ($),  then  the  number 
of  dollars,  then  a  period  (decimal  point),  then  the  number 
of  dimes,  and  then  the  number  of  cents. 

WRITTEN  EXERCISE 

Write  in  figures,  as  above:  1  dollar  and  5  cents, 
7  dollars  and  16  cents,  925  dollars  and  25  cents, 
17  dollars  and  50  cents. 


UNITED  STATES  MONEY  97 


ORAL  EXERCISE 
THE  SCHOOL  REGIMENT 

1.  The  flag  for  the  school  regiment  cost  $3.50  and 
the  drum  $4.     How  much  did  the  two  cost? 

2.  The  fife   cost  $3.     How  much  did  the  fife, 
the  drum,  and  the  flag  together  cost? 

3.  When  Charley  bought  the  flag  he  handed  the 
dealer  $4.     How  much  change  did  he  receive  ? 

4.  There  are   16  boys  in  the   regiment  besides 
the  officers.    Their  16  caps  cost  half  a  dollar  each. 
How  much  did  they  all  cost? 

WRITTEN  EXERCISE 

1.  If  the  16  boys  stand  4  in  a  line,  how  many 
lines  are  there  ?   Make  dots  on  paper  showing  how 
the  boys  are  placed. 

2.  If  the  16  boys  have  25-ct.  belts,  how  much 
did  the  belts  cost  for  the  4  boys  in  the  front  row? 
How  much  for  the  4  rows  ? 


98 


PRIMARY   ARITHMETIC 


ORAL  EXERCISE 

1.  Suppose  you  have  11  nickels.    Count  by  5's 
and  see  how  many  cents  you  have. 

2.  How  many  cents  make  7  nickels  ?   8  dimes  ? 

These  circles  show  the  size  of  the  most  common  coins. 


Cents 

3    A  NICKEL    5 
Nickel 


25  Cents 

A  QUARTER 
Silver 


We  add  dollars  and  cents  like  other  num-  $4.75 
bers,  writing  dollars  under  dollars,  dimes  under  2.29 
dimes,  and  cents  under  cents.  17.05 


WRITTEN   EXERCISE 


1.  $1.20  +  $2.00. 
3.  16.75  +  11.25. 


2.  |3.25  + 
4.  $1.06  + 


L05. 
5.07. 


MEASURES  99 

ORAL  EXERCISE 

1.  Can  you  tell  how  warm  it  is  by  looking  at  the 
thermometer?     Try  it.     Do  you  know  how  warm 
it  is  out  of  doors  to-day? 

2.  Do   you    know    at    what    temperature 
water  freezes?     At  what  temperature  does  it 
boil  ?    What  is  the  temperature  of  your  body  ? 

3.  Write  the  temperature  of  the  room  on 
the  blackboard.     Subtract  32  degrees  from 
this  to  see  how  much  it  is  above  freezing. 

4.  You  write  32   dollars   like  this:    $32. 
You  write  32  feet  like  this  :  32  ft.    Can  you 
tell  how  we  usually  write  32  degrees? 

You  have  told  the  teacher,  or  the  teacher  has 
told  you,  that  water  freezes  at  32  degrees,  written 
32° ;  water  boils  at  212°;  the  temperature  of  the 
body  is  about  98°. 

WRITTEN  EXERCISE 

1.  How  many  degrees  from  32°  to  212°, 
from  water  freezing  to  water  boiling? 

2.  How  many  degrees  from   32°  to    98°, 
from  water  freezing  to  your  temperature? 

3.  If  it  is  52°  in  the  Eskimo  boy's  snow 
hut,  and  is  68°  in  your  school,  how  much 
warmer  is  it  where  you  are? 

4.  If  it  is  18°  outdoors  where  the  Eskimo  boy 
lives,  and  is  65°  outdoors  to-day  where  you  live, 
how  much  warmer  is  it  where  you  are  ? 


100  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  Which  of  these  three  triangles  has  an  obtuse 
angle?     What  kind  of  a  triangle  is  this? 


2.  Which  has  a  right  angle?     Point  to  the  right 
angle.     What  kind  of  a  triangle  is  this? 

3.  In  which  of  the  triangles  are  all  of  the  angles 
acute?     What  kind  of  a  triangle  is  this? 

4.  Take  3  narrow  strips  of  paper  3  in.,  4  in,,  and 
5  in.  long.     Place  them  so  as  to  make  a  triangle. 
What  kind  of  a  triangle  is  it? 

A  triangle  having  a  right  angle  is  a  right-angled 
triangle. 

A  triangle  having  an  obtuse  angle  is  an  obtuse-angled 
triangle. 

A  triangle  having  three  acute  angles  is  an  acute-angled 
triangle. 

WRITTEN  EXERCISE 

1.  How  far  is  it  around  a  triangle  whose  sides 
are  14  ft.,  12  ft.,  and  12ft.? 

2.  Draw  an  acute-angled  triangle  with  two  of 
its  sides  2  in.  and  3  in.     Measure  the  third  side 
and  find  how  far  it  is  around. 

3.  Draw  a  right-angled  triangle  with  the  shortest 
side  1J  in.,  the  next  longer  side  2  in.     Measure 
and  find  the  length  of  the  longest  side. 


MEASUKES  101 

ORAL  EXERCISE 

1.  This  picture   shows  a  marble  floor  made  of 
pieces  1  ft.  square.     How  many  square  feet  are 
there? 

2.  How  many  yards  long  is  it 
on  each  side?     We  may  call  this 
what  kind  of  a  square? 

3.  How  many  square  feet  are 
there  in  1  square  yard?      Then 
1  sq.  ft.  is  what  part  of  1  sq.  yd.? 

As  there  are  square  inches  and  square  feet,  so  there 
are  square  yards,  square  rods,  and  square  miles.  You 
have  just  found  that 

9  square  feet  =  1  square  yard  (sq.  yd.). 

WRITTEN  EXERCISE 

1.  Draw  a  square  4  in.  on  a  side.     Show  how 
many  square  inches  it  contains. 

2.  Draw  a  picture  of  a  square  2  ft.  on  a  side, 
using  J  in.  for  a  foot.     How  many  square  feet  in 
the  square? 

This  is  called  drawing  to  a  scale  of  i  in.  to  1  ft. 

3.  Draw  a  picture  of  an  oblong  2  yd.  wide  and 
3  yd.  long,  on  a  scale  of  1  in.  to  the  yard.     How 
many  square  yards  in  the  oblong? 

4.  It  is  12  in.  around  a  square.     What  is  the 
length  of  each  side?     How  many  square  inches 
does  the  square  contain? 


102 


PRIMARY   ARITHMETIC 


ORAL  EXERCISE 

1.  If  each   of  these  blocks  is  1  ft.  square,  how 
many  square  feet  in  the  lower  row? 

2.  How  many  rows  are  there  ?  How 
many  square  feet  are  there  in  all  ? 

You  have  found  that  the  lower  row  con- 
tains 3  times  1  sq.  ft.  Therefore,  in  4  rows 
there  are  4  times  3  sq.  ft.,  or  12  sq.  ft. 

In  finding  areas,  we  write  either 

4  times  3  times  1  sq.  ft.  =  12  sq.  ft. 
or  4  times  3  sq.  ft.  =  12  sq.  ft., 

using  x  to  express  the  multiplication. 

WRITTEN  EXERCISE 

A  man  in  Dayton,  Ohio,  set  to  work  with  his  boys  to 
make    their  yard 
into  a  little  park. 

1.  It  was  30 

yd.  long  and  9 
yd.  wide.  What 
was  the  area? 

2.  The    walk 
was    3  ft.  wide 

and   it  ran   the    length  of    the  lot.       How  many 
square  feet  of  walk? 

3.  He  used  70  sq.  yd.  for  shrubbery.     You  have 
found  the  area  of  the  lot  and  of  the  walk.     How 
many  square  yards  were  left  for  lawn? 


CUBIC   MEASURE 


103 


PAPER   FOLDING 

1.  Draw  this  figure  8  times  as  large.    Cut  it  out 
and   fold  the  paper  along   the    dotted 

lines.     Make    a    cube    by   pasting    the 
shaded  strips. 

2.  Draw  this  figure  8  times  as  large. 
Cut  it  out  and  fold  the  paper  along  the 
dotted  lines.    Make  a  prism  by  pasting 
the  shaded   strips.     Can  you  see  how 
many  cubic  inches  this  prism  contains? 

3.  Draw  this  figure  8  times  as  large. 

Cut  it  out  and  fold  the  paper  as  before,  making  a 
prism.  This  prism  is  how  many 
times  as  large  as  the  other  one? 
How  many  cubic  inches  does  it 
contain? 

4.  You  have  now  learned  how  to 
fold  cubes  and  prisms.     Draw  the 


plan  for  a  cube  that  shall  be  2  in.  on  an  edge. 
Fold   the   cube.      How    many   cubic 
inches  does  it  contain? 

5.  Cut  and  fold  the  paper  to  make 
a  cubical  box  1  in.  on  an  edge. 

6.  Cut  and  fold  the  paper  to  make 

a  prism  that  is  4  in.  by  2  in.  by  3  in.    How  many 
cubic  inches  does  it  contain? 

Schools  that  do  not  have  the  facilities  for  paper  folding  may 
omit  the  few  exercises  in  which  it  is  required.  For  schools  that 
do  give  such  work,  these  exercises  will  suggest  others. 


104  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  How  many  cubic  inches  in  a  block  1  in.  long, 
1  in.  wide,  and  1  in.  high? 

2.  How  long  is  the  edge  of  a  cubic 
foot?   of  a  cubic  yard? 

We  write  cu.  in.  for  cubic  inch  or  cubic  inches;  cu.  ftc 
for  cubic  foot  or  cubic  feet. 

3.  Let  us  make  it  3  times  as  long.     How  many 
cubic  inches  in  a  block  3  in.  long,  1  in.  wide,  and 
1  in.  high? 

4.  Let  us  make  it  twice  as  wide.     How  many 
cubic  inches  in  a  block  3  in.  long,  2  in.  wide,  and 
1  in.  high? 

5.  Let  us  make  it  4  times  as  high.     How  many 
cubic  inches  in  a  block  3  in. 

long,  2  in.  wide,  and  4  in. 
high? 

Since  a  block  1  in.  long, 
1  in.  wide,  and  1  in.  high  con- 
tains 1  cu.  in.,  a  block  3  times  as  long  contains  3  times 

1  cu.  in.  =  3  cu.  in.,  and  a  block  2  times  as  wide  contains 

2  times  3  cu.  in.  =  6  cu.  in.,  and  a  block  4  times  as  high 
contains  4  times  6  cu.  in.  =  24  cu.  in. 

6.  How  many  cubic  inches  in  a  block  2  in.  long, 
2  in.  wide,  and  1  in.  thick?    Suppose  it  were  3  in. 
thick? 

For  this  page  and  the  next,  teachers  should  use  inch  cubes  of 
wood,  obtainable  from  dealers  in  kindergarten  material. 


CUBIC   MEASURE  105 

ORAL  EXERCISE 

1.  What  is  the  sum  of  all  the  edges  of  an  inch 
cube? 

2.  What  is  the  sum  of  all  the  edges  of  a  2-in. 
cube? 

3.  What  is  the  area  of  all  the  six  sides  of  an 
inch  cube? 

4.  What  is  the  area  of  all  the  six  sides  of  a  2-in. 
cube? 

5.  How  many  cubic  inches  in  a  2-in.  cube?   in  a 
3-in.  cube? 

WRITTEN  EXERCISE 

1.  How  many  cubic  inches  in  a  block  5  in.  long, 

3  in.  high,  and  3  in.  wide? 

2.  How  many  cubic    feet    in  a  _| 
ditch  11  ft.  long,  2  ft.  wide,  and 

4  ft.  deep? 

3.  How  many  cubic  feet  in  a  cupboard  8  ft.  long, 
4  ft.  wide,  and  3  ft.  high? 

4.  How  many  cubic  inches  in  a  lunch  box  6  in. 
long,  5  in.  wide,  and  3  in.  deep?     How  many  square 
inches  on  the  outside? 

5.  How  many  cubic  inches  in  a  drawer  8  in.  by 
4  in.,  and  3  in.  deep?     How  many  square  inches 
on  the  inside  ? 

6.  Measure  the  inside  of  a  crayon  box  in  inches 
and  find  its  volume  and  the  area  of  the  inside 
(including  the  cover). 


106  PRIMARY   ARITHMETIC 

FRACTIONS 
ORAL  EXERCISE 

1.  If  we  cut  an  apple  into  halves,  and  each  half 
into  halves,  we  have  cut  the  apple  into  what  parts  ? 

2.  We  therefore 
see  that  |-  of  J  of 
an  apple  is  what 
part  of  an  apple? 

3.  How    many 
fourths  are  ^  -f  \  +  -^?      How  do  you  write  this? 

The  teacher   should  copy  these  col-      o         tj        i  A        o^ 
umns  on  the  board,  a  pupil  writing  the 
sum  under  each.  '  ^ 

3      7      10      25 

4.  At  12  ct.  a  yard,  how  much     ~       ^      -i  n      «r 

will!  yd.  of  cloth  cost?    \  yd.? 

|  yd.?    (Point  to  J,  \,  and  f  of  the  3  column.) 

5.  At  28  ct.  a  yard,  how  much  will  \  yd.  cost? 
\  yd.?  f  yd.?     (Use  the  7  column.) 

6.  At  40  ct.  a  dozen,  how  many  oranges  can  be 
bought  for  20  ct.?     How  much  will  \  doz.  cost? 
f  doz.?     (Use  the  10  column.) 

7.  At  $1  a  bushel,  how  much  will  \  bu.  of  apples 
cost?    \  bu. ?    f  bu.?     How  many  pecks  can  you 
buy  for  75  ct.?     (Use  the  25  column.) 

WRITTEN   EXERCISE 

1.  Write  in  figures :  three  fourths,  two  thirds, 

2.  Howmuchis  \  of  24?  \  of  24?  \  of  40?  \  of  60? 


THIRDS,    FOURTHS,    FIFTHS 


107 


If  you  represent  A 


ORAL    EXERCISE 

1.  What  part  of  the  sphere  is  B?     Then  how 
many  fourths   of   a  sphere 

is  A?     How  do  you  write 
the  fraction? 

2.  If  you  call  the  sphere 
what  is  A?  B?    If  you  rep- 
resent B  by  1?  what  is  A? 
by  1,  what  is  B? 

3.  If  the  sphere  weighs  8  oz.?  how  much  does  B 
weigh?    A? 

4.  If  in  these  groups 
of  cubes   you    represent 
C  by  1,  what  is  B?     If 
Bis  l,what  is  A?    If  A 
is  1,  what  is  B? 

5.  Looking  at  B  and 

A?  1  —  I  =  how  many  fourths?    1  —  f  =  how  much? 

6.  Point  to  £  of  C ;  to  1  of  C.     Show  that  1  of 
C  =  f  of  C. 

7.  How  many  thirds  are  ^  +  ^? 
Show  this  by  the  picture. 

8.  How  much  is  1  —  ^?     1  —  f  ?     Show  this  by 
the  picture. 

,....,      9-  How  mnch  is  i  +  i ?    I  +  F 
|  +  |?     Show  this  by  the  picture. 

10.  How  much  is  1  in.  —  f  in.  ?  1  in.  —  |  in.  ?  |  in. 
- -^  in.?     Show  this  by  the  picture. 


108 


PRIMARY   ARITHMETIC 


75 
88 
67 
96 
54 
43 


ADDITION 

In  adding  long  columns,  write  the  sum  of  each 
column  separately.     You  can  then 
check  the  work  more  easily. 

Business  men  usually  add  up  the 
first  time,  and  check  the  result  by 
adding  down. 

Remember  to  read  a  column  like 
a  word.  You  do  not  spell  a  word  ;  33  sum  of  units 

39         u     u  tens 

you  read   it   by  syllables  if  it   is 

J  J      J  423  total  sum 

long. 

So  when  you  see  this  column 
your  eyes  should  catch  the  two  10's 
at  once  and  you  should  see  that  the 
sum  is  two  10's  and  6,  or  26. 

Add  rapidly;  you  will  make 
fewer  mistakes.  Group  by  10's 
or  other  numbers. 

WRITTEN   EXERCISE 

1.  49  2.  78 

87  32 

31  53 

53  46 

64  11 


10 


128 

4.  641 

5.  302 

62 

127 

87 

27 

143 

21 

48 

59 

63 

263 

42 

97 

6.  3152  7.  4172  8.  1247 

2237    1296     263 

468     327     602 


9.  $2.76  10.  $1.42 
2.94  3.76 
3.15  4.93 


SUBTRACTION  109 

SUBTRACTION 

ORAL  EXERCISE 

Subtract  rapidly,  stating  first  the  units,  then  the 
tens,  and  so  on,  finally  stating  the  answer.  Do  not 
repeat  the  numbers;  simply  tell  the  results. 

l.  74        2.  96      3.  $8.65      4.  92          5.  57 
43  75  6.40  70  42 


6. 

45 
24 

7. 

98 
24 

8. 

5800 
1600 

9. 

79 
54 

10. 

62 
41 

The  above  numbers  and  the  following  explanation  should  be 
written  on  the  board.  No  explanations  of  the  decimal  point  are 
needed  here.  Children  should  add  and  subtract  in  money  prob- 
lems as  with  integers. 

As  with  3-figure  numbers  (see  page  85), 

This  shows  all  the  work:  But  we  write  only  this: 

1632-1500  +  120  +  12  1632 

756  =    700+    50+6  756 

800+    70+    6-876  876 

Remember  that  to  check  the  work,  you  add  the  subtra- 
hend and  remainder;  the  sum  should  equal  the  minuend. 

WRITTEN   EXERCISE 

subtract : 

1.  8659  2.  8651  3.  8651  4.  $86.51  5.  $80.00 
4231    4239    4479    48.79     48.79 

6.  6535  7.  2800  8.  4327  9.  $90.21  10.  $50.27 
4176    177    1009     7.53      6.35 


110  PRIMARY   ARITHMETIC 

WRITTEN  EXERCISE 

1.  487  +  1263  +  1079.      2.  728  +  2693  + 1982. 
3.  1028  +  2347  +  3687.    4.  2983  +  1789  +  2864. 
5.  2009  +  1874  +  2096.    6.  4027  +  1089  +  1987. 
7.  1423  +  1346  +  4892.    8.  3276  +  2483  +  1872. 
9.  3248  +  3821  +  1924.  10.  2708  +  2873  +  1296. 

11.  There  are  5280  ft.  in  a  mile,  and  2640  in  a 
half  mile;  how  many  feet  in  1J  mi.? 

12.  A  man  started  in  business  with  $5500.     He 
saved  $ 750  the  first  year  and  $875  the  second. 
How  much  did  he  have  in  all  at  the  end  of  the 
second  year? 

Make  problems  for  Exs.  13-16,  and  find  the 
answers : 

13.  5280  ft.     14.  $2575     15.  $1575     16.  $4500 
2640  575  1275  625 
1320                 1425            2010  795 

17.6723-594.    18.6201-732.    19.7826-948. 
20.  $650  +  $75.   21.  $429  +  $86.   22.  $347  +  $95. 
23.  $826 -$78.    24.  $432 -$69.    25.  $321 -$46. 
26.4826-2938.  27.8072-6993.  28.3468-1896.- 
29.2987-1799.  30.5707-4902.  31.2093-1735. 
32.  3702-2075.  33.  6270-5295.  34.  3742-2981. 
35.4805-2967.  36.4083-3078.  37.2681-1692. 
38.5120-1635.  39.2009-1927.  40.3942-2875. 
41.  6000-1750.  42.  1700-1296.  43.  4073-1492. 
44.  7001-1992.  45.  8111-7888.  46.  8101-5909. 


REVIEW  111 


WRITTEN   EXERCISE 

1.  Jof  68.  2. 'lof  86.  3.  1  of  64. 

4.  i  of  66.  5.  £  of  39.  6.  £  of  63. 

7.  |  of  48.  8.  i  of  80.  9.  |  of  84. 

10.  !  of  55.         11.  |  of  500.       12.  i  of  550. 
13.  488  •+•  4.         14.  248  -  2.        15.  866  -  2. 
16.  804  H-  4.         17.  606  -«-  2.        18.  606  -*•  3. 
19.  3  times  66.    20.  4  times  48.   21.  5  times  77. 
22.  2802  -  1763.  23.  6023  -  4927. 

24.  1489  -  1093.  25.  4807  -  3096. 

26.  2986  -  1897.  27.  6096  -  2599. 

28.  2084  -  1975.  29.  4923  -  2876. 

30.  8426  -  2498.  31.  6800  -  4975. 

32.  8090-7099.  33.  7027-2975. 

34.  6203  -  3496.  35.  9800  -  2899. 

36.  $4027  -  $967.  37.  $8900  -  $987. 

38.  $4.67  +  $3.84.  39.  $2.95  +  $4.68. 

40.  $2.96 +  $1.98.  41.  $1.78 +  $4.96. 

42.  $3.48  +  $2.63.  43.  $2.69  +  $3.48. 

44.  275  +  68  +  8000  +  873. 

45.  123  +  98  +  2075  +  673. 

46.  342  +  87  +  1273  +  929. 

47.  298  +  75  +  3026  +  873. 

48.  375  +  42  +  2083  +  176. 

49.  186  +  37  +  1029  +  199. 

50.  187  +  92  +  2040  +  796. 

51.  892  +  28  +  4872  +  635. 

52.  176 +  39 +.2893 +  742. 


112 


PRIMARY   ARITHMETIC 


COUNTING   BY   DIFFERENT   NUMBERS 

ORAL  EXERCISE 

1.  How  many  cubes  in  each  column? 

2.  If  each  cube  weighs  6  oz.,  what  is  the  weight 

of  A?     of   B?     of  C? 
ofD?    ofE?    ofF? 
3.  Which    column 


shows 
of  6? 


of  6    blocks? 
of  6?        of 


6?   f  of  6?    What  does 
each  equal? 

4.  How  many  sides 
has  a  cube?  How 
many  sides  have  both 

cubes  of  B?   all  3  cubes  of  C?     Count  rapidly  the 
sides  of  all  the  cubes  in  the  columns  from  A  to  F. 


6 


The  teacher  should  write  on  the  board 
columns  of  6's  up  as  far  as  ten  6's,  the 
pupils  adding  each  column.  Here  are  five 
such  columns. 


5.  From  the  columns  on  the 
board  you  see  that  6  is  ^  of  what 
number?    ^  of  what  number? 

|  of  what  number? 

6.  You  also  see  that  12  is  ^  of  what  number? 
|  of  what  number?     Also  that  18  is  f  of  what 
number?    1J  times  what  number?    Tell  two  other 
number  facts  about  these  columns. 


6 
of 

6 
6 

what 

6     6 
666 
666 
666 

iramber? 

COUNTING   BY   SIXES  113 

ORAL  EXERCISE 

1.  Count  by  6's  from  0  to  .60,  thus : 

0  6  12  18  24 

30         36  42  48  etc. 

Count  again,  saying,  "  One  6  is  6,  two  6's  are  12, 
three  6's  are  18,"  and  so  on. 

2.  Count  in  this  way:  "In  6  there  is  one  6,  in 
12  there  are  two  6's,"  and  so  on  to  60. 

3.  State  rapidly  the  value  of  each  of  the  following : 


1x6          6x1 
2x6          6x2 
3x6          6x3 
4x6          6x4 
5x6          6x5 

4.  State  rapidly  the 

6-6           6-«-l 
12-6         12  +  2 
18-6         18-3 
24-6         24-4 
30-6        30-5 

6x6 
7x6 
8x6 
9x6 
10x6 

value  of  each  of 

36-6 
42-6 
48-6 
54-6 
60-6 

6x   6 
6x   7 
6x   8 
6x9 
6x10 

the  following 

36-6 
42-7 
48-8 
54-9 
60-10 

WRITTEN   EXERCISE 


1.  Copy  Exs.    3  and   4    above,   and   write  the 
answers. 

2.  Multiply  by  6 :  40,  41,  51,  70,  81. 

3.  Divide  by  6  :  $36,  42  ft.,  54  ct.,  48  yd. 


114 


PRIMARY   ARITHMETIC 


WRITTEN   EXERCISE 


Add  the  products  in  Exs.  1-24- 


1.  5  x  6  and  2x3.  2. 

3.  2  x  5  and  4x3.  4. 

5.  5x2  and  2x6.  6. 

7.  3  x  5  and  5x3.  8. 

9.  4  x  2  and  4x3.  10. 

11.  6x4  and  4x5.  12. 

13.  2  x  3  and  3x6.  14. 

15.  9x2  and  8x2.  16. 

17.  7x3  and  5x3.  18. 

19.  4  x  6  and  9x6.  20. 

21.  9x1  and  8x5.  22. 

23.  6  x  4  and  9  x  4.  24. 


4  x  2  and  3  x  4. 
3  x  3  and  4  x  4. 
3x4  and  5x4. 

2  x  6  and  3  x  6. 

3  x  5  and  4  x  6. 
6  x  7  and  6  x  2. 
3x3  and  4x5. 
8  x  3  and  7  x  4. 

6  x  2  and  9  x  3. 
8  x  2  and  7  x  2. 

7  x  3  and  8  x  2. 

8  x  5  and  9  x  5. 


25.  At  5  ct.  each  for  oranges  and  3  ct.  each  for 
bananas,  what  will  7  oranges  and  6  bananas  cost? 

26.  In  this  recess  game  Chester's  first  score  was 

four  6'sandtwo 
3's.  How  much 
was  this  score? 
27.  His  third 
score  was  three 
6's  and  three  3's. 
How  much  was 
this  score? 

This  forms  an  in- 
teresting game,  the 
numbers  being  changed  from  time  to  time.  Such  games  should, 
however,  not  take  time  from  the  rapid  drill  work. 


COUNTING   BY   SEVENS  115 


ORAL  EXERCISE 

1.  Count  by  7's  from  0  to  70.     Count  again, 
saying,  "  One  7  is.  7,  two  7's  are  14,"  and  so  on. 

2.  Count  in  this  way :    "  In  7  there  is  one  7, 
in  14  there  are  two  7's,"  and  so  on  to  70. 

3.  State  rapidly  the  value  of  each  of  the  following : 


1x7 

7x1 

6x7 

7x   6 

2x7 

7x2 

7x7 

7x   7 

3x7 

7x3 

8x7 

7x   8 

4x7 

7x4 

9x7 

7x   9 

5x7 

7x5 

10x7 

7x10 

4.  State  rapidly  the  value  of  each  of  the  following 

7-7 

7-1 

42-7 

42-6 

14-7 

14-2 

49-7 

49-7 

21-7 

21-3 

56-7 

56-8 

28-7 

28-4 

63-7 

63-9 

35-7 

35-5 

70-7 

70-10 

WRITTEN  EXERCISE 

1.  Copy   Exs.    3    and  4   above,  and  write   the 
answers. 

2.  Multiply  by  7 :    30,  61,  43,  25,  24,  35,  92, 
67,  49. 

3.  Divide   by    7:    63,   42,    $56,    28ft.,    49  in., 
70yd. 

4.  If  35  children  are  playing  a  game,  and  |  of 
them  are  hiding,  how  many  are  not  hiding  ? 


116  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  A  class  has  been  weaving  mats  like  this. 
How  many  horizontal  strips  ?  How  many  vertical 
ones?  How  many  in  all? 

2.  You  see  8  meshes  on  each  line. 
How  many  are  there  on  2  lines?  on 
3?  on  4?  on  5? 

3.  Walk    rapidly,    counting    8    for 
each  step  until  you  reach  80.   How 
many  steps  did  you  take? 

4.  State  rapidly  the  value  of  .each  of  the  following : 


1x8 
2x8 
3x8 
4x8 
5x8 

5.  State 
8-8 
16  +  8 
24-8 
32-8 
40-8 

8x1 
8x2 
8x3 
8x4 
8x5 

rapidly  the  value 
8-1  ' 
16-2 
24-3 
32-4 
40-5 

6x8          8x6 
7x8          8x7 
8x8          8x   8 
9x8          8x   9 
10x8          8x10 

of  each  of  the  following  : 
48-8        48-6 
56-8        56-7* 
64-8        64-8 
72-8        72-9 
80-8        80  -10 

6.  Tell  the  numbers  from  9  to  18,  each  increased 
by  8 ;  each  decreased  by  8. 

WRITTEN  EXERCISE 

Copy  Exs.  4  and  5  and  write  the  answers. 


COUNTING   BY   NINES 


117 


ORAL   EXERCISE 


1.  Count  by  9's  from    0  to  90.  '  Count  again, 
saying,  "  One  9  is  9,  two  9's  are  18,"  and  so  on. 

2.  Count  in  this  way:  "In  9  there  is  one  9,  in 
18  there  are  two  9's,"  and  so  on  to  90. 

3.  State    rapidly    the    value    of    each    of    the 
following : 


1x9 

9x1 

2x9 

9x2 

3  x  9 

9x3 

4x9 

9x4 

5x9 

9x5 

6x9 

9x6 

7x9 

9x7 

8x9 

9x8 

9x9 

9x9 

10  x  9 

9x10 

4.   State    rapidly  the   value    of    each    of    the 


following : 

9-9 
18-9 
27-9 
36-9 
45-9 


9-1 

18-2 
27-3 
36-4 
45-5 


54-9  . 

54-6 

63-9 

63-  7 

72-9 

72-8 

81-9 

81-9 

90-9 

90-10 

WRITTEN  EXERCISE 

1.  Copy   Exs.   3    and   4    above   and   write   the 
answers. 

2.  Multiply  by  9:  30,  37,  67,  27,  46,  49. 

3.  Divide  by  9:  $81,  90ft.,  63  in.,  54  bu. 

4.  How  many  yards  of  ribbon  at  9  ct.  a  yard 
can  be  bought  for  45  ct.  ? 


11>  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  Count  by  10's  from  0  to  100,  as  you  have 
counted  by  other  numbers. 

2.  Give  the  tables  of  10*s,  as  you  have  of  other 
numbers. 

3.  How  much  is  10  times  7?     10  times  55? 
10  times  600?  10  times  725?    What  short  way 
have  you  found  for  multiplying  by  10? 

4.  How  much  will  10  oranges  cost  at  5  ct.  apiece? 
at  6  ct.  apiece?  at  4  ct.  apiece? 

5.  How  much  will  10  yd.  of  cloth  cost  at  9  ct. 
a  yard?  at  3  ct.  a  yard?  at  12  ct.  a  yard? 

6.  There  are   100  years   in   a  century.     How 
many  years   are  there  in   10   centuries?   in   20 
centuries? 

7.  How  many  school  days  in  2  weeks?     If  you 
are  in  school  5  hours  a  day,  how  many  hours  will 
you  spend  in  school  in  2  weeks?  in  4  weeks? 

8.  If  in  4  weeks  you  spend  100  hours  in  school, 
how  many  hours  will  you  spend  in  40  weeks,  or 
10  times  4  weeks? 

WRITTEN    EXERCISE 

Write  the  tables  of  10's,  as  you  did  the  tables 
of  9's. 

Besides  frequent  drill  in  counting  by  different  numbers 
beginning  with  0,  pupils  should  learn  to  count  by  4's,  beginning 
with  1,  2,  or  3,  and  by  5's,  beginning  with  1,  2,  3,  or  4. 


liULTIHJCATIOH    TAKLK    RKVJKVVKO 


119 


REVIEW   OF   THE   MULTIPLICATION   TABLE 

You  have  now  learned  how  to  multiply  together  any  two 
numbers  of  one  figure  each. 

Since  2x1=1x2,  we  need  give  only  one  of  these 
products. 

1X1=1 
2X1=2 
3X1  =  3  3x2  =  6  3x3  =  9 

4x3  =  12 

5X3  =  15 

6x3  =  18 


4X1  =  4 
5x1=5 
6x1^6 


2x2=4 
3x2  =  6 
4x2  =  8 
5x2  =  10 
6x2  =  12 
6X6=36 
7x1=7      7x2  =  14      7x3  =  21 

7x6  =  42      7X7=49 
8x1=8     8x2=16      8X3  =  24 

8x6  =  48      8x7  =  56      8x8  =  64 
9x1-9      9x2  =  18      9X3  =  27 

9x6  =  54      9X7  =  63      9x8  =  72       9x9  =  81 

In  the  following  table  the  product  of  any  left-hand  num- 
ber and  top  number  is  opposite  the  first  and  under  the  second. 


4X4  =  16 
5X4  =  20 
6x4  =  24 

5x5  =  25 
0x5  =  30 

7x4-28 

7x5  =  35 

8x4  =  32 

[ 

8x5  =  40 

9x4  =  36 

9X5  =  45 

1 

2 

0 

4 

6 

6 

7 

8 

9 

10 

1 

1 

2 

3 

4 

5 

0 

7 

8 

9 

10 

2 

2 

4 

6 

8 

10 

}-2 

14 

16 

18 

20 

3 

3 

6 

9 

12 

15 

L8 

21 

24 

27 

30 

4 

4 

8 

12 

16 

20 

24 

28 

32 

36 

40 

5 

5 

10 

15 

25 

30 

35 

40 

45 

50 

6 

6 

12 

18 

24 

30 

30 

42 

48 

54 

60 

7 

7 

14 

21 

28 

35 

42 

49 

56 

63 

70 

8 

8 

16 

24 

32 

40 

48 

56 

64 

72 

80 

9 

9 

18 

27 

36 

45 

54 

63 

72 

81 

90 

10 

10 

20 

30 

40 

50 

60 

70 

80 

90 

100 

Counting  by  1's 
"  "  2's 
"  "  3's 


"  6's 

"  7's 

44  8»B 

"  9's 

"  10's 


120  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  State  the  multiplication  table  of  2's ;  of  3's ; 
of  4's;  of  5's. 

.2.  State  the  multiplication  table  of  6's;  of  7's; 
of  8's;  of  9's. 

3.  I  am  thinking  of  two  numbers  whose  product 
is  18.     What  may  the  numbers  be? 

4.  I  am  thinking  of  two  numbers  whose  product 
is  30.     What  may  the  numbers  be? 

5.  I  am  thinking  of  two  numbers  of  one  figure 
each  whose  product  is  20.     What  are  the  numbers? 

6.  You  know  that  2  times  11  are  22,  and  3  times 
11  are  33.     It  is  therefore  very  easy  to  count  by 
ll's.     Give  the  multiplication  table  of  ll's. 

This  figure  may  be  drawn  on  the  black- 
board and  made  the  basis  of  interesting  exer- 
cises. Write  some  number  in  the  center  and 
let  the  children  tell  the  products  as  one  of  the 
class  points  to  the  outer  numbers.  Instead  of 
products,  the  children  may  tell  the  products 
increased  by  some  number,  as  2  or  3. 

WRITTEN   EXERCISE 

1.  Write  the  multiplication  table  of  ll's  men- 
tioned in  Ex.  6,  above. 

2.  Write  the  2's  from  2  to  20,  and  under  them 
write    the    12's         2,    4,     6,    8,  and  so  on  to    20. 
from  12  to  120.        12,  24,  36,  48,  and  so  on  to  120. 

3.  Write  the  multiplication  table  of  12's  with 
the  help  of  Ex.  2. 


MULTIPLICATION  121 

MULTIPLICATION 

ORAL  EXERCISE 

Multiply,  stating  first  the  units,   then  the  tens, 
and  so  on.    Do  not  repeat  the  numbers  multiplied. 

1.     11        2.     21        3.     40        4.     70        5.     90 

_7  _5  _6  J8  _9 

6.  Ill       7.  305        8.  407        9.  509       10.  612 

__7  _6  _8  _9  _5 

The  above  examples  should  be  written  on  the  blackboard. 

As  with  smaller  numbers  (page  87),  so  in  multiplying 

438  by  6,  we  might  multiply  the  438 

units,   tens,   and    hundreds    sepa-  6 

rately  and  add  the  products.    But  48  =  6  times     8 

this  would  make  the  work  too  long.  180  =  6      "      30 

We  therefore  say:  "  6  times  8  are  48  2400  =  6      "    400 

(writing  8) ;  6  times  3  (tens)  are  18  2628  -  6      «    438 

(tens),  and  1 8  +  4  =  22  (writing  2) ;  Wriu  Qnly  Ms  . 

6  times  4  (hundreds)  are  24  (hun-  4gg 

dreds)  and  24  +  2  =  26."  6 

All  such  explanations  must  be  devel-  2628 

oped  at  the  blackboard,  but  children  should  not   be   asked  to 
repeat  them. 

WRITTEN   EXERCISE 


Multiply: 
1.  63  by  5. 
4.  96  by  6. 
7.  85  by  9. 
10.  287  by  6. 

2.  72  by  6. 
5.  98  by  7. 
8.  63  by  7. 
11.  407  by  7. 

3.  87  by  7. 
6.  88  by  8. 
9.  126  by  5. 

12.  827  by  8. 

122  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  The  land  of  this  farm  is  worth  $70  an  acre. 
In  one  of  the  pastures  there  are  9  acres.  How 
much  is  this  pasture  worth  ? 


2.  There  is  another  pasture  of  8  acres.     How 
much  is  that  one  worth?      How   much  would  a 
6-acre  pasture  be  worth? 

3.  There  are  20  cows  kept  on  the  farm,  and  each 
gives  an  average  of  5  qt.  of  milk  a  day  through  the 
year.     This  averages  how  many  quarts  a  day  for 
the  farm? 

4.  At  wholesale  this  milk  brings  2  ct.  a  quart. 
How  much  is  the  average  daily  income  from  the 
milk?    How  much  does  this  amount  to  in  a  week? 

WRITTEN   EXERCISE 

1.  If  the  farmer  makes  butter  instead  of  selling 
the  milk,  it  will  take  the  cream  of  3  gal.  to  make 
1  Ib.  of  butter.    How  many  pounds  could  be  made 
daily  from  24  gal.  ? 

2.  If  he  sells  this  butter  for  23  ct.  a  pound,  how 
much  will  be  his  daily  income  from  butter? 


2.  55-5. 

3.  555-5. 

5.  560-7. 

6.  560-8. 

8.  630-9. 

9.  639-9. 

11.  720-8. 

12.  7200-8 

14.  810-9. 

15.  8100-9 

DIVISION  123 

DIVISION 

ORAL  EXERCISE 
1.     50-5. 

4.  56-7. 

7.  63-9. 

10.  72-8. 

13.  81-9. 

16.  7)4900  +  140  +  7.  17.  8)2400  +  160  +  16. 

As  with  smaller  numbers  (see  page  90),  you  may  think 
of  the  number  to  be  divided  as  separated  into  parts. 
Thus,  to  divide  522  by  6,  you  may  think: 
"  I  do  not  know  the  quotient  of  500-^-6,  nor 
of  520  -4-  6,  but  because  48  -^  6  -  8  I  know 
that  480-^6  =  80,  leaving  42  to  be  divided;   I  know 
that  42  -^  6  =  7.    Therefore,  the  quotient  is  87." 

Teachers  will  find  it  helpful  to  use  either  the  long-division  or 
the  annexed  form  in  developing  this  process,     f*\Ao(\       jo 
changing  to  the  short-division  form  as  soon  as        '- 

Qf\      I          rr 

the  children  have  discovered  the  reasons  for 

the  steps.     Formal  explanations  should  not  be  =87 

required  at  this  time. 

WRITTEN  EXERCISE 

1.  275-5.              2.  375-5.  3.  685-5. 

4.  486-6.              5.  552-6.  6.  744-6. 

7.  924-7.              8.  833-7.  9.  854-7. 

10.  816-8.  11.  744-8.  12.  632-8. 

13.  3330-9.  14.  4230-9.  15.  8919-9. 

16.  4278-3.  17.  2048-8.  18.  5735-5. 


124  PRIMARY   ARITHMETIC 

The   divisions  thus  far   have    been  exact ;   that  is, 
8-^-2  =  4  exactly.     But  if  we  try  to  divide 
9  by  2,  we  have  9  -*-  2  -  4,  and  one  left  over. 

The  part  left  over  in  division  is  called  the  remainder. 

In  dividing  by  7  we  see  that  7  is  contained  in  14 
twice;  in  17,  twice  and  3  over;  in  16,  twice  and  2  over; 
in  27,  three  times  and  6  over. 

ORAL   EXERCISE 

Divide  the  numbers  in  the  columns  by  the  divisor 
given,  in  Exs.  1-6: 


1. 

45-5 

2.  37-6 

3.  50- 

7 

26 

41 

35 

30 

23 

48 

27 

34 

63 

4. 

64-8 

5.  82-9 

6.  72- 

10 

32 

72 

30 

44 

62 

45 

51 

52 

27 

When  there  is  a  remainder  a  fraction  is  written  in 
the  quotient,  thus:  45 -*- 4  =  11,  with  1  still  to  be 
divided ;  and  1  -*-  4  =  \.  Therefore,  45  H-  4  =  11 1. 

4)87  3)92  8)68 

21f  30f  8|  or  8^ 

State  the  quotient,  including  the  fraction: 
7.  43-4.  8.  41-2.  9.  31-3. 

10.  36-5.  11.  56-5.  12.  81-4. 

13.  83-4.  14.  22-4.  15.  23-2. 


DIVISION  125 

ORAL  EXERCISE 

State  rapidly  the  results  in  Exs.  1-8: 

1.  56-8,  56  -  7,  7  x  8.  2.  81-9,  9  x  9. 

3.  42-6,  42-7,  7x6.  4.  64-8,  8x8. 

5.  54-9,  54-6,  9  x  6.  6.  49  -  7,  7  x  7. 

7.  48-8,  48-6,  6  x  8.  8.  36-6,  6  x  6. 

9.  How  does  the  dividend  compare  with  the 
product  of  the  divisor  and  the  quotient? 

10.  If  the  product  of  the  divisor  and  the  quo- 
tient equals  the  dividend,  what  does  this  tell  about 
your  work  ? 

From  Exs.  9  and  10,  you  have  found  that,  if  the  work 
is  correct,  the  product  of  the  quotient  and  divisor  equals 
the  dividend. 

When   we   divide    75    by    9    we     9)75 
say  that  the  quotient  is  8  and  the  8>  3  remainder, 

remainder  is  3.     That  is,  72-^9  =  8.     Therefore, 

If  there  is  a  remainder,  subtract  this  from  the  dividend 
before  checking  your  work. 

WRITTEN  EXERCISE 

In  these  examples,  check  the  work  by  multiplying 
the  quotient  by  the  divisor: 

1.  4866-6.         2.  5754-7.         3.  6976-8. 
4.  9009-7.         5.  1233-9.         6.  7005-5. 

7.  If  9  carriages  cost  $1125,  what  does  each  cost? 

8.  If  there  are  224  pupils  in  8  classes,  how  many 
are  there  on  an  average  in  each  class? 


126  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

Sailors  are  not  afraid  to  approach  our  shores  at  night, 
because  the  lighthouses  warn  them  of  danger  and  direct 
them  to  harbors  of  safety.  The 
government  has  built  these  light- 
houses along  the  coasts.  A  fog 
horn  is  blown  when  there  is  a  fog. 

1.  Have  you  ever  seen  a  light- 
house ?   If  so,  tell  the  class  about 
it.     About  how  high  was  it? 

2.  The  government  has  1332 
lighthouses,  and  45  light-ships 
near  dangerous    shoals.      How 
many  of  both? 

3.  On  dangerous  reefs  there 
are  buoys  that  whistle  or  ring 

a  bell.     We  have  90  whistling  buoys  and  130  bell 
buoys.     How  many  of  both? 

WRITTEN   EXERCISE 

1.  Some  lights  are  made  to  flash  every  2  seconds, 
being  bright  2  sec.  and  then  dark  2  sec.     How 
many  times  does  such  a  light  flash  in  1  min.  ? 

2.  How   many   times    does   this   light  flash   in 
1  hr.  ?     How  many  times  from  6  P.M.  to  6  A.M.? 

3.  A  powerful  light  burns  2  gal.  of  oil  a  night. 
How  many  does  it  burn  in  a  year  of  365  days? 

4.  At  20  ct.  a  gallon,  how  much  does  the  oil  cost 
for  one  night  ?  for  one  week  ?  for  four  weeks  ? 


REVIEW 


127 


WRITTEN   EXERCISE 

Florida  and  California  are  the  great  orange-growing 
states  of  our  country.  This  is  a  picture  of  one  of  the 
California  groves. 

1.  This  is  what  it  cost  a  man  in  California  to 
go  into  orange 

growing : 

10  acres  of 
orange  land, 
$7  50;  building 
a  small  house, 
$  500  ;  a  well, 
$25.50;  wind- 
mill, $35.75; 
pump,  $15; 
water  tank,  $50;  horse,  $50;  1000  orange  trees, 
$600;  tools  and  fencing,  $65.25.  What  was  the 
total  cost? 

2.  He   paid  out  for   help,   during   the  5  years 
before  the  trees  began  to  bear,  the  following  sums: 
$27.50,    $25.75,    $19.40,    $23.30,   and   $21:50. 
What  is  the  total  of  these  5  payments? 

3.  The  first  year  that  the   trees  bore   he  sold 
1500  boxes  of  oranges  at  $1  a  box  and  1200  at 
$2  a  box.     How  much  did  he  receive  in  all? 

4.  In  one   week   he   paid    $13.45  for   cartage, 
$16.50  for  labor,  $18.50  for  boxes,  and  $38.75  for 
express.     What  was  the  total  amount? 


128  PRIMARY   ARITHMETIC 

WRITTEN   EXERCISE 

Add  in  Exs.  1-6 : 


1. 

$2341.00 

2.  $4817.20 

3.  $1263.40 

1026.25 

280.50 

487.50 

1248.32 

175.25 

25.00 

543.00 

1028.30 

620.05 

268.16 

426.40 

35.15 

4. 

$1200.00 

5.  $3147.25 

6.  $5234.00 

47.50 

23.30 

48.75 

620.00 

5162.00 

162.00 

3.75 

29.30 

2348.05 

41.75 

4.75 

9.25 

27.32 

125.00 

16.42 

Subtract  in  Exs.  7-1 4 : 
7.  2487         8.  4893         9.  1798         10.  3492 
1693  2987  1699  1976 

11.  $83.75    12.  $87.62    13.  $926.35    14.  $962.75 
46.57  48.75  887.26  598.36 

Multiply  in  Exs.  15-20: 

15.  $426  by  7.  16.  $327  by  9.  17.  $463  by  5. 

18.  $265  by  8.  19.  423  ft.  by  6.  20.  628  yd.  by  4. 

21.  2864  -  4.   22.  3115  -  5.  23.  6006  -  7. 

24.9864-8.   25.4111-3.  26.3575-2. 

Since  the  change  of  a  single  figure  in  any  of  the  above  problems 
entirely  changes  the  example,  a  page  like  this  furnishes  much 
opportunity  for  drill  by  changing  a  few  numbers. 


COUNTING  129 

II.    OPERATIONS  REVIEWED.     SPECIAL  ATTENTION 
TO  MULTIPLICATION  AND  DIVISION 

COUNTING  REVIEWED 

ORAL  EXERCISE 

1.  Count  by  2's  from  2  to  100;  from  1  to  99. 
Which  takes  the  longer? 

2.  Count  to  100  by  3's,  beginning  with  0;  with  1; 
with  2. 

3.  Count  to  100  by  4's,  beginning  with  0;  with  1; 
with  2;  with  3. 

4.  Count  to  100  by  5's,  beginning  with  0;  with  1; 
with  2;  with  3;  with  4. 

5.  'In  the  same  way,  count  by  6's,  beginning  with 
0  or  any  number  less  than  6. 

6.  In  the  same   way,  count  by  9's,  beginning 
with  0  or  with  any  number  less  than  9. 

7.  Count  to  100  by  7's;  by  8's;  by  ll's;  by  12's. 

WRITTEN  EXERCISE 

1.  Write  the  6's  of  Ex.  5. 

2.  Write  the  9's  of  Ex.  6. 

Exs.  1  and  2  constitute  the  new  matter,  the  rest  being  review 
work. 

3.  Write  the  3's  of  Ex.  2. 

4.  Write  the  4's  of  Ex.  3. 

5.  Write  the  5's  of  Ex.  4. 


130  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

Read  the  numbers : 

1.  V,  X,  L,  C.  2.  IV,  IX,  XL,  XC. 

3.  VI,  XI,  LI,  LXI.       4.  XIX,  XXIX,  XLIX. 

5.  Where  have  you  seen  the  Roman  numerals 
used  ?  Why  are  they  harder  to  work  with  than 
our  common  numerals? 

You  will  have  but  little  need  for  Roman  numerals. 
Sometimes  they  are  used  for  dates,  and  this  is  the  only 
need  you  will  have  for  large  numbers  written  in  this 
way. 

D  means  500,  and  M  means  1000. 

Then  we  write 

C,  CC,COC,CD,  D,  DC,  DCC,  DCCC,  CM,   M, 
for  100,200,  300,  400,500,600,  700,     800,     900,1000. 

Hence  we  write 

CCLXIfor261,    CDXIX  for  419,    DCCCLX  for  860, 
CMIV  for  904,      MD  for  1500,         MCM  for  1900. 

The  Romans  more  often  wrote  MDCCCC  for  1900,  but  now 
it  is  usually  shortened  to  MCM. 

It  should  be  remembered  that  the  pupil  will  have  little  use 
for  these  numerals  except  in  reading  chapter  numbers. 

WRITTEN  EXERCISE 

1.  Write  in  Roman :  562,  743,  827,  329,  101. 

2.  Write    in    common    numerals :    CCCXXIII, 
CDLTX,  DCCLXXV1I,  GDI,  DCCCVIII. 

3.  Write  in  common  numerals  the  number   of 
this  year. 


ADDITION  .      131 


ADDITION 
ORAL  EXERCISE 

Add  rapidly  in  Exs.  1-10 : 


1.  36 

2.  47 

3.  35 

4.  12 

5.  11 

43 

42 

34 

85 

83 

6.  48 

7.  52 

8.  74 

9.  82 

10.  59 

61 

53 

43 

74 

60 

State  at  sight  the  sums  in  Exs.  11-15 : 
11.   $19     12.   $15     13.   $17      14.   $19      15. 

_A        _§         -Jl         -1         _§ 

The  teacher  should  give  frequent  oral  drills  of  this  kind. 

Add  rapidly  : 

16.     14     17.     27      18.     32      19.     48      20.     73 
352          402  556  241  124 

In  writing  a  column  of  numbers  representing  dollars 
and  cents,  you  have  seen  that  the  sign  $  is  placed  before 
the  first  number  and  the  result  only.  You  have  also 
seen  the  same  for  numbers  expressing  units  like  feet 
and  pounds.  When  written  in  a  horizontal  line  the  sign 
is  used  with  each  number,  thus :  $2  +  $3  +  $10  =  $15. 

WRITTEN  EXERCISE 

1.  $2.73  +  $4.96  +  $5.75  +  $3.49. 

2.  $4.87 +  $14.92 +  $25 +  $17.64. 

3.  $100 +  $175.50 +  $325 +  $4.75. 


132      9  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 
SOME  HOME  MEALS 

1.  The  coffee  for  our  breakfast  cost  6  ct.,  the 
potatoes  4  ct.,  the  meat  32  ct.,  and  the  bread  4  ct. 
How  much  did  the  bread  and  meat  cost?     How 
much  did  all  the  food  cost? 

2.  The  oatmeal  for  a  breakfast  cost  8  ct.,  the 
milk  4  ct.,  the  fruit  10  ct.,  the  rolls  and  butter 
5  ct.,  and  the  eggs  8  ct.     How  much  did  this  food 
cost? 

3.  For  a  dinner  the  meat,  cost  30  ct.,  the  vege- 
tables 20  ct.,  the  dessert  20  ct.,  the  coffee  15  ct., 
and  the  other  food  15  ct.     Find  the  total  cost. 

4.  The  meals  for  a  small  family  cost  $1.70  on 
one  day  and  $2.20  on  another  day.     How  much 
did  they  cost  for  these  two  days  ? 

WRITTEN  EXERCISE 

Add: 

1.  $3.04  2.  $3.40  3.    $34.45  4.  $45.75 

6.03  6.30  63.35  34.50 

7.04  7.40  74.45  29.86 

5.  $127.00   6.  $49.80   7.  $286.00     8.  $480.00 

42.30  8.65  431.00  275.00* 

69.90  4.32  125.50  496.00 

40.00  15.00  62.75  52.50 

8.75  4.00  148.00  7.70 


SUBTRACTION  133 

SUBTRACTION 

ORAL  EXERCISE 

Subtract : 

1.  353   2.  462   3.  780   4.  690    5.  187 
121     240     630     370       45 

6.  $4.75  7.  |350  8.  $280  9.  $4.50  10.  $6.35 
.25     50     20     .40      .30 

Write  the  above  examples  and  the  following  explanation  on 
the  board  as  usual.  Frequent  oral  drills  of  this  kind  should  be 
given. 

In  subtracting  $176.75  from  $247.50, 

You  may  think  this:  But  write  only  this: 

$247.50  =  $100  +  $140  +  $6  + 150  ct.         $247.50 
176.75  =   100+     70+6+    75  176.75 

$70          +    75  ct.  $70.75 

That  is,  in  subtracting  United  States  money,  write  the 
decimal  points  in  a  column  and  subtract  the  numbers  in 
the  usual  way. 

WRITTEN  EXERCISE 

l.  $24.75 -$6.90.          2.  $35.50 -$17. 
3.  $145.10  -  $75.50.       4.  $129 -$0.75. 

5.  A  man's  income  was  $1500  and  his  expenses 
were  $1275.     How  much  did  he  save? 

6.  A  man's  salary  was   $1400  a  year,  and  he 
received  $180  from  a  house  that  he  rented.     His 
expenses  were  $1142.     How  much  did  he  save? 


134  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  7654  2.  9860  3.  4863  4.  5957  5.  1283 
-231   -7340   -2541   -2845    -101 

Pupils  should  be  required  to  state  such  differences  quickly, 
without  taking  time  to  repeat  the  numbers.  Frequent  drills 
on  such  blackboard  problems  should  be  given. 

In  the  written  exercise  following,  and  in  similar  cases,  the 
element  of  time  is  important.  Unduly  slow  work  is  usually 
inaccurate.  The  pupil  always  has  a  simple  test  of  accuracy  in 
checking  by  addition. 

WRITTEN   EXERCISE 


Subtract  : 

1. 

5. 

$72.41 
24.92 

2.  $29.84 
12.97 

3.  $94.76 
76.98 

4.  $60.70 
55.81 

$50.01 

6.  6542 

7.  9008 

8.  5286 

20.09 

5997 

2519 

2394 

9.  7629  10.  8536  11.  7629ft.  12.  1436yd, 
7537      687      6289      563 

13.  7024  Ib.  14.  9673  gal.  15.  $8841  16.  9527 
1065     7796       7952     986 

17.  3342  18.  4763  19.  2696  20.  6000 
929      824      1727     4236 

21.  $21.40  22.  $40.00  23.  $90.00  24.  $24.00 
17.52      5.75      36.27      .78 


REVIEW 


135 


ORAL    EXERCISE 

1.  Ralph  is  training  his  company  for  the  Fourth. 
They  have  bought  a  dozen  boxes  of  caps  at  2  ct. 
a  box,  and  10  guns  at  50  ct.  each.     How  much 
did  they  pay  for  the  caps  and  the  guns  ? 

2.  Jim,  who  carries  the  flag,  bought  a  gun  and 
8  boxes  of  caps.     How  much  did  these  cost  him? 


3.  Will,  who  plays  the  drum,  has  bought  3  big 
firecrackers  at  6  ct.  each.     He  handed  the  dealer 
a  quarter.     How  much  change  did  he  get? 

4.  Jack  had  20  ct.?  and  he  bought  3  packs  of 
5-ct.  firecrackers,  and  bought  a  big  firecracker  with 
the  rest.     How  much  did  this  firecracker  cost? 

5.  George  paid  36  ct.  for  a  dozen  big  firecrackers. 
How  much  were  they  apiece  ?    What  would  8  cost  ? 

6.  The  company  collected  $2.50  for  10  pieces  of 
fireworks.    What  was  the  average  cost  of  each? 


136  PRIMARY   ARITHMETIC 

MULTIPLICATION 

ORAL   EXERCISE 

I.  State  the  results  as  the  teacher  points  to  the 

numbers. 

Each  figure  should 
be   drawn    upon    the 
blackboard,  the  num- 
/70    ber  in  the  center  being 

,  frequently  changed,    i 

14 

2.  How    much 
is  3  times  $12?   3  times  $1.20?   3  times  $0.12? 
3.  How  much  is  8  times  $11?  8  times  $1.10? 

To  multiply  United  States  money,  multiply  as  with 
other  numbers,  placing  the  decimal  point  after  <jto  OK 
the  dollars.  o 

In  this  example,  3  times  5  ct.  =  15  ct. ;  3    '*.„  *r 
times  20  ct.  =  60  ct.,  which  with  the  10  ct.  = 
70  ct.;  3  times  $2  =  $6.    Therefore,  the  product  is  $6.75. 

WRITTEN   EXERCISE 

Multiply  in  Exs.  1-9:. 

1.  $2.25  by  5.     2.  $2.25  by  4.     3.  $4.75  by  3. 

4.  $14.92  by  6.   5.  $1205  by  8.    6.  $8.93  by  9. 

7.  $3.02  by  7.  8.  $23.46  by  8.  9.  $12.05  by  8. 
10.  At  $10.50  a  ton,  how  much  will  7  tons  of  hay 
cost? 

II.  At  $0.83  a  bushel,  how  much  will  7  bu.  of 
wheat  cost  ? 


MULTIPLICATION  137 

ORAL  EXERCISE 

1.  Multiply  by  10  :  2,  20,  25,  125. 

2.  Multiply  by  10  :  20  ct.,  $1.00,  $1.20,  $2.25, 
$3.50. 

3.  Multiply  by  10:  $3.00,  $3.75,  $14.00,  $35.50, 
$2.00,  $2.50. 

Because  10  times  25  is  250,  and  10  times  $2.25  is 
122.50,  therefore, 

To  multiply  by  10,  annex  a  zero.  If  there  is  a  decimal 
point,  move  it  one  place  to  the  right. 

Although  10  times  25  ct.  =  250  ct.,  the  result  is 
usually  written  $2.50,  and  so  for  similar  cases. 

25         32 

The  work  in  multiplying  by  numbers       "QQ          QQO 

ending  in  0  is  usually  arranged  like  this:       ^QQ       9(KK) 


WRITTEN  EXERCISE 

1.  At  30  ct.  a   dozen,  how  much  will  10  doz. 
pencils  cost? 

2.  At  35  ct.  a  box,  how  much  will  10  boxes  of 
crayons  cost? 

3.  At  10  ct.  apiece,  how  much  will  2  doz.  black- 
board pointers  cost? 

4.  At  10  ct.  a  small  package,  how  much  will 
half  a  dozen  small  packages  of  pens  cost? 

5.  How  many  fingers  in  a  class  of  27?     How 
many  toes  ?     How  many  fingers  and  toes  ? 

6.  If  an  arithmetic  costs  35  ct.,  how  much  must 
be  paid  for  10  arithmetics?  for  2?  for  a  dozen? 


138  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  The    class   made    some    needlebooks.     Each 

cover  had  12  gray  strips 
of  paper  and  ^  as  many 
red  ones.  How  many  red 
ones? 

2.  The  red  strips  were 
6  in.  long,  and  the  gray 
ones  were  ^  as  long.    How  long  were  the  gray  ones? 

3.  The  strips  were  ^  in.  wide.     How  long  was 
the  book?     How  wide?     How  many  square  inches 
on  this  side  of  the  cover?  on  all  the  outside? 

4.  The  flannel  leaves   are  ^  in.  less  in  length 
and  J  in.  less  in  width  than  the  cover.     How  long 
are  they  ?     How  wide  ? 

5.  They  bought  ^  yd.  of  flannel  for  the  leaves 
at  50  ct.  a  yard.     How  much  did  it  cost? 

6.  It  takes  |  yd.  of  ribbon  to  tie  each  book. 
How  many  can  be  tied  with  1  yd.?   with  2  yd.? 
with  4  yd.? 

7.  How  many  strips   of  gray  paper  would  be 
needed  for  10  books?     How  many  of  red  paper? 

8.  The  paper  cost  1  ct.  for  4  books.    There  were 
40  books  made.     How  much  did  all  of  the  paper 
cost? 

9.  The  ribbon  for  tying  the  leaves  cost  2  ct.  a 
yard,  and  ^  yd.  was  used  for  each  book.     How 
much  did  the  ribbon  cost  per  book?  for  40  books? 


MULTIPLICATION  139 

ORAL   EXERCISE 

1.  2  times  5  and  3  times  5  are  how  many  times  5? 

2.  20  times    7  and  3   times   7  are  how   many 
times'  7? 

3.  20  times  326  and  3  times  326  are  how  many 
times  326? 

You  have  found  that  23  times  326  is  the  sum  of  20 
times  326  and  3  times  326.  Therefore,  to  multiply 
326  by  23, 

You  may  think  this:  But  write  only  this: 

326  326 

23  J23 

978  product  by  3          978 
6520    u    u  20         652 

7498    "    "  23         7498 

WRITTEN   EXERCISE 

Multiply  in  Exs.  1-15: 


1. 

127 

2. 

402 

3. 

350 

4. 

252 

5. 

317 

13 

21 

32 

35 

42 

6. 

237 

7. 

635 

8. 

522 

9. 

398 

10. 

129 

43 

14 

11 

19 

67 

11.  At  $275  an  acre,  how  much  will  27  acres  of 
garden  property  cost? 

12.  A  dealer  buys  1  doz.  typewriters  at  $82  each, 
and  sells  them  at  $100  each.    What  does  he  gain? 


140  PRIMARY    ARITHMETIC 

ORAL    EXERCISE 

1.  Multiply  by  3 :  7,  70,  10,  11,  12,  9,  900. 

2.  Multiply  by  4:  40,  400,  30,  300,  70,  §  700. 

3.  Multiply  by  6:    2,  $2,  2  ct.,   $2.02,  $3.03, 
$4.04,  $6.06. 

4.  Multiply  by  8 :    3,  $3,  10  ct.,  $3.10,  $3.06, 
$5.07,  $9.08. 

In  multiplying  $2.35  by  27, 

This  shows  all  the  work:  But  we  write  only  this : 

$2.35  $2.35 

27  27 

$16.45  product  by  7  1645 

47.00    "    "  20  47  0 

$63.45    "    «  27  $63.45 

WRITTEN   EXERCISE 

Multiply  in  Exs.  1-10: 
1.  $4.82  by  15.  2.  $3.27  by  22. 

3.  $4.09  by  19.  4.  $3.96  by  21. 

5.  $2.81  by  38.  6.  $1.39  by  39. 

7.  $2.99  by  27.  8.  $1.75  by  34. 

9.  $0.69  by  72.  10.  $0.75  by  32. 

11.  At  $24  a  dozen,  how  much  will  24  silver 
tablespoons  cost?   9?   33? 

12.  At  $36  a  dozen,  how  much  must  a  dealer 
pay  for  4  cut-glass  vases?   for  16? 

13.  Three    armchairs    can   be   bought  for    $21. 
At  this  rate,  how  much  will  14  such  chairs  cost? 


MULTIPLICATION 


141 


WRITTEN    EXERCISE 


Did  you  ever  see  men  harvest  ice  ?     After  it  has 
frozen  10  or  12  inches  thick  it  is  cleared  of  snow  by  a 


scraper  drawn  by  a  horse,  and  then  split  or  sawed.  The 
cakes  are  then  packed  in  an  ice  house,  covered  with 
sawdust,  and  kept  until  summer. 

1.  How  many  square  feet  of  frozen  surface  are 
there  on  a  pond  260  ft.  long,  having  an  average 
width  of  30  ft.? 

2.  If  the  ice  is  12  in.  thick,  how  many  cubic 
feet  of  ice  can  be  cut  from  the  pond? 

3.  Ice  weighs  62  Ib.  per  cubic  foot.    What  is  the 
weight  of  one  of  these  cakes  of  ice  1  yd.  square, 
the  ice  being  1  ft.  thick? 

4.  Not  all  of  the  ice  of  Ex.  2  is  sold.     A  quarter 
is  lost  in  cutting  and  by  melting.     How  many  cubic 
feet  are  lost? 


142  PRIMARY   ARITHMETIC 

DIVISION 
ORAL  EXERCISE 

1.  How  much  is  i  of  10  ? 


2.  How  many  2's  in  10  ?     II  II  II  II  II. 

3.  How  many  $2  bills  are  worth  $10  ?   $20? 

4.  How  many  2's  in  12?  in  16  ?  in  20?  in  40? 
.  5.  How  much  is  J  of  $12?   J  of  16  ft.? 

Because  2  ft.  -I-  2  ft.  +  2  ft.  -  6  ft.,  or  3  times  2  ft. 
=  6  ft.,  we  see  that 

1.  2  ft.  is  contained  3  times  in  6  ft. 

2.  If  6  ft.  are  separated  into  3  equal  parts,  there 
are  2  ft.  in  each  part ;  that  is,  J  of  6  ft.  =  2  ft. 

The  teacher  may  find  it  advisable  to  postpone  the  following 
discussion  of  division. 

There  are,  therefore,  two  kinds  of  division : 

1.  Measuring,  as  when  we  measure  6  ft.  by  2  ft. 
Thus,  6  ft.  -4-  2  ft.  =  3. 

2.  Separating,  as  in  separating  6  ft.  into  3  equal  parts. 
Thus,  \  of  6  ft.  =  2  ft.,  or  6  ft.  -^  3  =  2  ft. 

WRITTEN  EXERCISE 

Divide,  putting  the  dollar  signs  in  the  right  places: 
1.  $648-8.      2.  $756  -*- $4.      3.  $6304-8. 
4.  $8748-9.    5.  $4830- $7.    6.  $3003- $7. 

7.  If  one  barrel  of  apples  cost  $4,  how  many 
barrels  can  be  bought  for  $284? 

8.  If  4  car  loads  of  apples  cost  $3200,  how  much 
will  one  car  load  cost  ?     How  much  will  7  cost  ? 


DIVISION  143 

ORAL  EXERCISE 

1.  204-2.     2)$2  +  4ct.     $2.04-2. 

2.  609-3.     3)$6  +  9ct.     $6.09-3. 

3.  $8.40  -*•  4,  $5.50  -*-  5,  $6.66  -  6,  $8.08  *  8. 

4.  How  many  times  is  $2  contained  in  $200? 

5.  How  many  times  is    $6  contained  in  $66? 
6ft.  in  66ft.?   6bu.  in  66  bu.? 

You  have  seen  that  $2.04  +  2  =  $1.02.     That  is, 
To   divide    United  States  money,  divide  in  the  usual 
way,  placing  the  decimal  point  after  dollars'  place  in  the 
quotient. 

For  example,  in  dividing  $17.28  by  6,  we  see  that 
we   cannot  exactly  divide  $17  by  6,  but     p \db-i  7 '90 
$12  -s-  6  =  $2,  leaving  $5.28  to  be  divided.        }        ' 
We  cannot  exactly  divide  52  dimes  by  6, 
but  48  dimes  -5-6  =  8  dimes,  leaving  48  ct.  to  be  divided. 
48  ct.  -s-  6  =  8  ct.     Therefore,  the  quotient  is  $2.88. 

As  on  page  123,  teachers  are  advised  to  develop  this  work  first 
by  using  the  long-division  form,  changing  to  the  form  above  given 
as  soon  as  the  operation  is  understood. 

WRITTEN  EXERCISE 

1.  $17.28-8.  2.  $17.28-4.  3.  $27.93-3. 
4.  $16.40-8.  5.  $37.44-9.  6.  $42.35-7. 
7.  $326.25-9.  8.  $13.20-6.  9.  $17.28-12. 

10.  If  3  head  of  cattle  cost  $82.50,  how  much  will 
1  head  cost?     How  much  will  10  head  cost? 

11.  If  8  barrels  of  apples  cost  $36,  how  much 
will  1  barrel  cost?    How  much  will  5  barrels  cost? 


144  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  HowmanylO'sin20?  in  50?  in  500?  in  600? 

2.  How   many   10's  in  450?  in  570?   in  680? 
in  1000? 

3.  If  a  number  ends  in  0,  how  can  you  easily  tell 
how  many  10's  it  contains? 

4.  How  many  2's  in  4?     2  ft.  in  4  ft.?     2  tens 
in  4  tens?     20's  in  40?     20's  in  400? 

5.  How  many  3's  in  9?  30's  in  90?  30's  in  900? 

6.  How  many  4's  in  36  ?  40's  in  360  ?  40's  in  3600 ? 

7.  Howmany5'sin35?50'sin350?  50'sin3500? 

8.  If  you  are  dividing  a  number  ending  in  0  by 
another  number  ending  in  0,  what  may  you  do 
with  both  O's? 

Therefore,  when  there  are  no  fractions, 

To  divide  a  number  ending  in  0  by  10,  simply  cancel 
theO. 

To  divide  a  number  ending  in  0  by  another  number 
ending  in  0,  cancel  a  0  at  the  end  of  each  and  divide. 

10)470  20) 580 

47  29 

WRITTEN   EXERCISE 


1.840-40. 
4.360-60. 
7.  1110-30. 

2.100-50. 
5.  750-50. 
8.  1330-70. 

3.  7000-20. 
6.  9600-30. 
9.  7280  -  80. 

10.  2220  -  60.   11.  1050  -  70.   12.  $6150  -  50. 
13.  $4140-|90.  14.  $2360-$40.  15.  $3040-$80. 


REVIEW 


145 


WRITTEN   EXERCISE 

Our  government  has  a  large  number  of  life-saving 
stations  along  our  coast.  Rescues  are  generally  made 
by  boat,  but  sometimes  by  a  line  fired  over  the  ship. 

1.  We  have  195  stations  on  the  Atlantic  and 

Gulf  coasts,  58 
on  the  Great 
Lakes,  16  on 
the  Pacific, 
and  1  on  the 
Ohio  river. 
How  many  are 
there  in  all? 

2.  In    one 
year  there  were  378 
wrecks,    averaging  8 
persons  in  each.    How  many 
were  in  these  wrecks? 
3.  Out  of  the  378  wrecks,  1  out  of 
every  9  resulted  in  the  loss  of  a  ship.   How 
many  ships  were  lost?     (How  many  9's  in  378?) 

4.  The   night   signals  warned   210    ships  from 
danger ;  the  day  signals  warned  -^  as  many.    How 
many  were  warned  by  both? 

5.  The  wreck  guns  were  used  to  fire  life  lines 
15  times.     On  each  of  6  times  1  shot  was  fired. 
Two   shots    were  fired    each  of   the  other  times. 
How  many  shots  were  fired  in  all? 


146  PRIMARY    ARITHMETIC 

ORAL  EXERCISE 

1.  How  many  ll's  in  22?  in  33?  in  77?  in  99? 

2.  How  many  ll's  in  11?  in  110?  in  550? 

3.  Divide  : 

11)550  +  22    11)660  +  33    11)7700  +  440 

4.  Divide  : 

11)3300  +  110  +  22     How  much  is  3300  +  110  +  22? 

Ex.  4  shows  that  we  may  separate  the  dividend  into 
parts  as  with  a  one-figure  divisor.  But  it  is  easier  to 
divide  like  this,  writing  the  quotient  at  the  top. 

This  is  the  complete  work  :  But  we  write  only  this  : 

312  312 

11)3432  to  be  divided  11)3432 

3300  -  300  times  11  33_ 

132  still  to  be  divided  13 

=  10  times  11  11 


_ 

22  still  to  be  divided  22 

22  =  2  times  11  22 

We  see    that    3000  -s-  11  =  no    thousands,    but   that 
3400  -s-  11  =  300,  and  100  +  32  remaining  to  be  divided  ; 

132  -s-  11  =  10,  and  22  still  remaining  to  be  divided; 
22  -*•  11  =  2.     Therefore,  the  quotient  is  312. 

WRITTEN  EXERCISE 


1.  231-11. 
4.  1232-11. 
7.  5346-*-  11. 

2.  561  +  11. 
5.  3762-11. 
8.  6006-11. 

3.  781-11. 
6.  9636-11. 
9.  7117-11. 

DIVISION  147 

ORAL  EXERCISE 

1.  2100-21.  21)2100  +  21  21)2100  +  42 

2.  3100-31.  31)3100  +  62  31)3100  +  620 

3.  4100-41.  41)4100  +  82  41)4100  +  410  +  82 

4.  6300-21.  21)6300  +  21  21)6300  +  420  +  21 

As  we  divided  by  11  (page  146),  so  we  may  divide  by 
other  numbers.     For  example,  divide  6741  by  21. 

The  teacher  is  advised  to  develop  on  the  board 
the  full  form,  as  on  page  146,  leading  the  children 
to  discover  the  successive  steps  and  to  state  simple 
reasons  for  taking  them.  The  unnecessary  figures 
should  then  be  erased,  leaving  the  form  here  shown. 
Children  should  not  be  asked  to  explain  the  process : 
it  is  sufficient  that  they  understand  it  as  presented, 
the  work  then  becoming  mechanical,  as  it  is  with 
adults.  The  explanation  given  on  page  146  may 
serve  as  an  outline. 

WRITTEN  EXERCISE 

1.  4935-21.       2.  2646-21.        3.  7287-21. 

4.  4898-31.       5.  3689-31.       6.  6758-31. 

7.  5125-41.  8.  4838-41.  9.  4879-41. 
10.  5049-51.  11.  5661-51.  12.  6273-51. 
13.  5429-61.  14.  7881-71.  15.  9477-81. 

16.  At  $11  each,  how  many  rocking-chairs  can 
be  bought  for  $385? 

17.  At  $31  each,  how  many  head  of  cattle  can 
be  bought  for  $589? 

18.  At  $71  each,  how  many  Texas  ponies  can  be 
bought  for  $1491? 


148  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  120-12,      1200-12. 

2.  12)1200  +  120,  12)2400  +  12. 

3.  12)3600  +  120,  12)3600  +  360  +  36. 

4.  220-22,  22)2200  +  22,  22)4400  +  66. 

5.  64-32,   32)6400  +  32,  32)6400  +  320  +  32. 

6.  84  -  42,   42)8400  +  42,  42)8400  +  420  +  84. 

7.  104-52,  1040-52,    52)1040  +  52. 

Examples  like  the  above  should  be  written  on  the  board  as 
usual.  They  lead  immediately  to  the  following  case  of  division. 
The  full  form  should  first  be  given,  as  suggested  on  page  147,  the 
unnecessary  figures  then  being  erased.  The  following  explanation 
may  serve  as  an  outline.  It  is  sufficient  at  this  time  to  consider 
only  two-figure  divisors  with  the  unit's  figure  0,  1,  or  2. 

Required  to  divide  3328  by  32. 

We  see  that  3000 -32 -no  thou- 
sands, but  3300  -32  -about  100,  so 
we  write  1  in  hundreds'. place.  Taking 
away  100  times  32,  there  is  still  128  to 
be  divided.  We  see  that  120  -  32  = 
no  tens,  and  we  write  a  0  in  tens'  place. 
There  is  still  128  to  be  divided,  and 
128-32-4. 

WRITTEN  EXERCISE 

1.  4836-12.  2.  6036-12.  3.  4824-12. 
4.  1224-12.  5.  6384-12.  6.  2'442-22. 
7.  3840-32.  8.  2142-42.  9.  5304-52. 


DIVISION  149 

ORAL  EXERCISE 

1.  510-51,         5100-51,        5200-52. 

2.  102-51,        1020-51,         1530-51. 
3.122-61,         1220-61,         1240-62. 

4.  142-71,        1420-71,         1440-72. 

5.  At    $72  a  head,  how  many  ponies  can  be 
bought  for  $144?  for  $1440? 

6.  At  $32  a  head,  how  many  head  of  cattle  can 
be  bought  for  $64?  for  $640?   for  $6400? 

Pupils  should  have  been  led  before  this  to  express  the  follow- 
ing statement  in  their  own  language.  It  is  here  inserted  as  a 
basis  for  comparison. 

You  have  seen  that  there  are  three  things  to  be  done 
in  division: 

1.  Write  each  quotient  figure  over  the  place  that  shows 
its  value,  as  over  the  hundreds  or  tens. 

2.  Multiply  the  divisor  and  this  quotient. 

3.  Subtract  this  product  and  proceed  as  before  until  a 
remainder  appears  that  is  less  than  the  divisor. 

Teachers  should  call  attention  to  the  fact  that  it  is  usually 
necessary  to  notice  only  the  first  two  figures  of  the  dividend  and 
the  first  figure  of  the  divisor  to  determine  the  quotient  figure. 
Also  that  it  is  necessary  to  bring  down  only  one  new  figure  of 
the  dividend  with  each  subtraction. 

WRITTEN  EXERCISE 

1.  4686-22.      2.  7700-22.      3.  5280-22. 

4.  6720-32.      5.  5460-42.      6.  7992-72. 

7.  9180-51.      8.  3796-52.      9,  8464-92. 


150  PRIMARY   ARITHMETIC 


ORAL  EXERCISE 

1.  At  20  ct.  a  dozen,  how  much  will  3  doz.  eggs 
cost?   5  doz.? 

2.  At  $4  a  dozen,  how  much  will  3  handker- 
chiefs cost? 

3.  At  21  ct.  a  dozen,  how  much  will  4  doz.  eggs 
cost?   3  doz.?   10  doz.? 

4.  At  23  ct.  a  dozen,  how  much  will  2  doz.  eggs 
cost?    3  doz.?    10  doz.? 

5.  At  $18  a  dozen,  how  much  will  18  cut-glass 
tumblers  cost? 

6.  At    $24    a  dozen,  how  much   will    10   fine 
linen  napkins  cost? 

7.  At  $9  a  dozen,  how  much  will  J  doz.  cups 
and  saucers  cost? 

8.  At  40  ct.   a  dozen,   how  much  will   3  doz. 
oranges  cost?   ^  doz.?    1J  doz.? 

9.  At   60  ct.    a  dozen,  how  much  will  J  doz. 
oranges  cost?     How  much  will  2  doz.  cost? 

10.  At  50  ct.  a  dozen,  how  many  oranges  can  be 
bought  for  $1?   for  $1.50?   for  $2? 

11.  At  22  ct.  a  dozen,  how  many  eggs  can  be 
bought  for  66  ct.?   for  11  ct.?   for  77  ct.? 

12.  At  30  ct.  a  dozen,  how  many  bananas  can 
be  bought  for  60  ct.?   for  15  ct.?   for  75  ct.? 

13.  At   30  ct.  a   dozen,  how  much  will  6  doz. 
bananas  cost?     At  25  ct.  a  dozen,  how  much  will 
4  doz.  cost? 


REVIEW 


151 


ORAL  EXERCISE 

1.  If  some  children  pay  45  ct.  for  a  Christmas 
tree  and  give  the 

dealer  $1,  how 
much  change  is 
due? 

2.  If  they  buy 
9  candy  canes  at 
8  ct.  each,  how 
much  will  they 
cost?  How  much 
change    should 
they  get  for 


3.  If  they  buy  their  mother  4  handkerchiefs  at 
25  ct.  each,  how  much  will  they  cost? 

4.  They  buy  10  colored  balls  at  4  ct.  each,  and 
5  strings  of  tinsel  at  5  ct,  a  string.    How  much  do 
both  cost? 

WRITTEN  EXERCISE 

1.  How  much  did  the  tree,  the  canes,  the  balls, 
and  the  tinsel  together  cost  ? 

2.  The  children  bought  21  doz.  candles  at  18  ct. 
a  dozen  for  the  tree.    How  much  did  they  cost? 

3.  They  bought  some  toys  costing  15  ct.,  23  ct., 
32  ct.,   30  ct.,  10  ct.,   25  ct.     How  much  did  all 
these  cost? 

4.  If  the  children  had  saved  $6.50  to  spend  for 
all  these  things,  how  much  was  left? 


152 


PRIMARY   ARITHMETIC 


FRACTIONS 


ORAL  EXERCISE 


1.  What  part  of  A  is  shaded?   of  B  ?   of  C  ? 

2.  Which     rect- 
angle  shows  that 


3.  Which  shows  that 


=  l?  that 


- 


4.  Calling  each  small  square  1,  which  rectangle 
shows  that  ^  of  6  =  1? 

5.  Which   shows  that        of  6  =  5  ?   that        of 


6-2?  that  i  of  6 -3? 


that  f  of  6  =  4? 


6.  In  what   other   ways    could   you  shade   the 
squares  in  A  to  show  J  ?   in  B  to  show  |  ? 

7.  Show   from    the   rectangles   that  J  +  J  =  f ; 


WRITTEN  EXERCISE 


1.  This  rectangle  shows,  that  1  —  i  =  f  . 
a  rectangle  showing  that  1  —  |  =  f  . 

2.  In  the  same  way  draw  rectangles 
showing  the  following  : 


Draw 


3.  Draw  rectangles  to  show  the  following: 


-i,         1-f, 


FRACTIONS 


153 


WRITTEN  EXERCISE 

1.  Jennie  made  a  button   box  for  her  mother. 
She  drew  this  plan,  cut  it  out,  and  folded  it  along 
the  dotted  lines.     Draw  the  plan, 

full  size. 

2.  She  covered  the  top  and  bot-/ 
torn  with  ribbon,  3J  in.  wide.    She\ 
bought  4  in.  for  each  side  of  the 
bottom,  and  14  in.  for  each  side 

of  the  top,  so  as  to  allow  for  turning  in. 
much  did  she  buy? 

3.  This   ribbon   cost    30  ct.   a 
yard.    How  much  did  it  all  cost? 

4.  She  covered  the  sides  with 
If  in.  ribbon,  plain  on  the  inside. 
How  much  did  she  need  for  the  in- 
side, allowing  1  in.  for  turning  in? 

5.  She  allowed  twice  as  much  for  the  outside  as 
for  the  inside.     How  much  did  she  use  for  both? 

6.  This  narrow  ribbon  cost  20  ct.  a  yard.     How 
much  did  she  pay  for  what  she  used? 

7.  Rose  made  a  bag  for  her  brother's  scarf  pins. 

She  took  a  piece  of  chamois  skin 
4^-  in.  by  6  in.,  and  marked  it  as 
in-  shown.  She  folded  A  over  B  and 
sewed  it  so  as  to  make  a  pocket, 
folding  C  down  for  a  cover, 
the  plan,  full  size. 


-4Hn 


Draw 


154 


PRIMARY   ARITHMETIC 


ORAL  EXERCISE 

1.  In  the  first  circle  state  rapidly  ^  of  the  num- 
ber to  which  the  teacher  points,  and  then  |  of  the 
number.  In  the  second,  state  ^  of  the  number, 
then  f . 

The  pictures  should  be  drawn  on  the  blackboard. 
9 


2.  To  find  |  of  a  number,  what  part  do  you 
first  find?     To   find  f  of   a   number,  what  part 
do  you  first  find?      How  would  you  find  -f  of  a 
number?   f  of  a  number? 

3.  How  would  you  find  f  of  a  number?    -^  of 
a  number  ?   ^  of  a  number  ?   ^  of  a  number  ? 

4.  You  have  seen  that  £  =  f  =  f  >  and  that  £  =  f . 
This  line  shows  that  |  =  how  many  j  .  ,  .  ,  .  ,  .  ,  .  | 
tenths  ? 

WRITTEN  EXERCISE 

Draw  lines  and  divide  them  into  parts  to  shoiv 
the  following : 


9. 


=  f.  2.  |  =  l.  3. 
=  f-  8.  t  =  f.  7. 
=  |.  10.  l  =  |.  11. 


4. 

8. 
12. 


FRACTIONS 


155 


ORAL  EXERCISE 

1.  How  many  are  J  of  a  dozen  rabbits  ? 
dozen?   i  of  a  dozen? 


of  a 


of  a  dozen  rabbits?    f  of  a 
dozen? 


of  a 


2.  How  many  are 
dozen?    ^  of  a  dozen? 

3.  How  many  are  f  of  a  dozen?    T] 
T52-  of  a  dozen  ? 

4.  State  £  of  24,  30,  40,  100.     Also  4 
|  of  30,  $  of  60,  |  of  60. 

5.  How  much  is  £  of  40?  f  of  40?  f  or 

6.  How  much  is  |   of  50?   f  of  50?   f 

7.  How  much  is  J  of  18?    f  or  £  of  18? 
of  18?    |  or  |  of  18? 

8.  How  many  minutes  in  \  hr.?    \  hr.? 

WRITTEN  EXERCISE 


of  24, 

of  40? 
of  50? 


f  hr.? 


1.  i  of  729,  |  of  729. 

2.  \  of  836,  f  or  \  of  836,  f  of  836. 

3.  \  of  235,  f  of  235,  f  of  235,  |  of  235. 

4.  i  of  732,  f  or  i  of  732,  f  or  \  of  732,  |  or  f 
of  732. 

5.  If  Ralph  drove  24  mi.  one  day,  and  Rob  drove 
f  as  far,  and  Harry  drove  f  as  far  as  Rob,  how  far 
did  Rob  and  Harry  each  drive  ? 


156  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  How  many  feet  are  1 J  ft.  +  |  ft.? 

2.  What  is  the  sum  of  J  +  J?   2J  +  1{?   3J  +  2{? 

3.  How  many  dollars  are  $|-  +  $J  +  $J?     How 
many  inches  are  f  in.  -f  J  in.? 

4.  What  is  the  sum  ofi  +  J  +  J?    of  £  +  J  ? 
of  If  +  |?   of  2f  +  3J?   of  4£  +  5£?   of  £  and  £? 

5.  How  much  is  $|  +  $|  +  ${  +  $£?     $f  +  $i? 

^Lrf^  the  following : 

6.  2£          7.  41         8.  6f  9.   5|         10.  2J 

J         .I         J          J          M 

WRITTEN  EXERCISE 

1.  Draw  a  5-in.  line,  marking  it  off  in  inches. 
Beneath  it  write  the  sums  of 

i  +  £,         i -f  I?         !  +  i?         t  +  f- 

2.  Draw  a  6-in.  line,  marking  it  off  in  inches. 
Beneath  it  write  the  sums  of 

3.  Draw  lines  showing  the  sums  of 


1921  246f 

47 
21f 


4.  Add: 

248^ 
409f 

423f 
201f 

620^ 

47 

FRACTIONS  .    157 

ORAL  EXERCISE 

1.  How  many  cents  in  J  of  a  dollar  ?    in  ^  of  a 
dollar?   in  f  of  a  dollar? 

2.  How  much  is  4  of  10?    i  of  100?   4  of  100  ct.? 

o  o  o 

I  of  a  dollar  ? 

3.  How  much  is    2    times    20  ct.?     f   of   $1? 
|  of  $1?   |  of  $1? 

4.  On  the  blackboard  divide  100  by  3.     How 
much  is  i-  of  $1? 

5.  On  the  blackboard  divide   100  by  6.     How 
much  is  i  of  $1? 

You  have  now  found  the  following : 
i-  of  $1  =  $0.50,  or  50  ct.         1  of  $1  =  $0.331,  or  331  ct. 
1  of  $1  =  $0.25,  or  25  ct.         1  of  $1  =  $0.20,  or  20  ct. 
l  of  $1  =  $0.16f ,  or  16|  ct.      |  of  $1  -  $0.75,  or  75  ct. 

WRITTEN  EXERCISE 

1.  From  f  of  $1  subtract  |  of  $1. 

2.  Add  :    i  of  $1  +  i  of  $1  +  £  of  $1. 

3.  Add  the  following: 

$0.50  $0.75  $0.25 

.25  .331  .50 

.16|  .16|  .75 

.20  .25  .20 


4.  Subtract : 

$1.00    $0.331    $1.00    $427.36 


.50      .131     .20     39.48 


158  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  In  this  picture,  if  B  represents  $1,  how  much 

is  represented  by  A? 
How  many  cents? 
2.  If    B   represents 
how  much  is  rep- 
resented by  C?     How  many  dollars  and  cents? 

3.  If  C  represents  90  ct.,  how  much  is  represented 
by  A?   byB?  by  A  +  B?   byA  +  B  +  C? 

4.  If  C  weighs  12  oz.,  how  much  does  A  weigh? 
B?  A  +  B?  A  +  C? 

5.  If  A  +  B  +  C  represents  1,  what  does  A  repre- 
sent?   B?    C?    A  +  B?    A  +  C?    B  +  C? 

The  actual  inch  cubes,  easily  procured,  offer  material  for 
abundant  exercise  of  .this  kind.  The  objects  should,  however, 
be  discarded  as  soon  as  they  cease  to  be  necessary,  the  simpler 
number  facts  of  fractions  then  being  memorized. 

WRITTEN  EXERCISE 

1.  In  the  picture,  if  the  cubes  are  of  iron,  and  C 
weighs  f  lb.,  how  many  ounces  does  A  weigh?   B? 

2.  If  C  weighs  1  lb.,  what  is  the  weight  of  A? 
of  B?  of  A  +  B?  of  A  +  C?  ofB  +  C?  of  A  +  B  +  C? 

3.  If  A  +  C  represents  $1,  what  sum  is  repre- 
sented by  A?  by  B?  by  C?  by  B  +  C? 

4.  If  these  cubes  were  ounces  of  gold,  B  would 
be  worth  $40.     How  much  would  A  be  worth? 
C?  A  +  C? 


FRACTIONS 


159 


ORAL  EXERCISE 


1.  If  you  have  3  ct.  and  spend  1  ct.,  how  much 
have  you  left?     If  you  have  -f-  of  a  dollar  and 
spend  |  of  a  dollar,  how  much  have  you  left? 

2.  -,  -,  -,  -. 


3.2- 


,     3f-f,       7f-5i     lOf-71. 

4.  How  much  is  left  if  you  take  ^  of  an  apple 
from  \  of  an  apple?     Then  how  much  is  |-  —  i? 


6.  If  you  have  $f  and  spend  $|-?  what  part  of 
a  dollar  have  you  left?    Then  how  much  is  f  —  J? 

7-  f-i        7|-i,      -7|-2J,        9f-5f 


WRITTEN  EXERCISE 

Subtract  in  Exs.  1-8: 
1.  273f         2.  648|         3.  467| 
47{  199^  188f 


5.  425f         6.  283J 


7.  632f 
287* 


9.  Rose  has  made  this  thread 
box.  It  is  4J  in.  long,  2  in.  deep, 
and  2  in.  wide.  How  many 
square  inches  of  silk  will  it  take 
to  line  it?  If  you  wish,  you  may 
make  a  paper  pattern. 


4.  129f 
391 


8.  500J 


160  PRIMARY   ARITHMETIC 

WRITTEN  EXERCISE 

1.  |  of  960.          2.  f  of  999.  3.  f  of  324. 

4.  f  of  564.  5.  |  of  720.  6.  f  of  916. 

7.  |  of  812.  8.  |-  of  444.  9.  f  of  507. 

10.  |  of  705.         11.  |  of  801.         12.  f  of  873. 

13.  Add  |  of  612  and  {  of  832. 

14.  From  f  of  804  take  f  of  171. 

15.  From  f  of  816  take  f  of  204. 

16.  42f  +  26£  +  33|  +  2f          17.  624f  -  127J. 
18.  17f +  18f +  26f +  2{.          19.  482f-127|. 
20.  21£  +  19£  +  18f  +  26.          21.  634|  -  293f . 
22.  16f  +  14|  +  2H  +  25.  23.  293£  -  198f . 
24.  29|  +  36f  +  18|  +  7|.  25.  926|  -  129f 
26.  42f +  26f  +  14|  +  6f  27.  200|  -  175f 
28.  25|  +  36f +  41|  +  63f         29.  498f  -  299f 
30.  31£  +  26£  +  23f +  41f.        31.  283f  -  168J.. 
32.  29|  +  63^  +  48|  +  81|.        33.  400|  -  193f 

34.  How  many  cubic  inches  in  a  box  8  in.  long, 
4  in.  wide,  3  in.  deep  ? 

Make  problems  for  Exs.  35-55,  and  find  the 
answers  : 

35.  2  x  5  x  17.  36.  3  x  9  x  11.  37.  4  x  8  x  12. 
38.  3  x  6  x  12.  39.  8  x  8  x  6.  40.  5  x  7  x  11. 
41.  624-3.  42.  827-2.  43.  634-5. 
44.  817-*- 4.  45.  422-3.  46.  2808-72. 
47.  3159-81.  48.  2418-62.  49.  2499  +  51. 
50.  4331-61.  51.  1312-32.  52.  1312-41. 
53.  2394-42.  54.  1508-52.  55.  5184-72. 


MEASURES  161 

MEASURES 
ORAL  EXERCISE 

1.  What  is  the  area  of  a  rectangle  3  ft.  long  and 
1  ft.  wide? 

2.  What  is  the  area  of  a  rectangle  3  times  as 
wide?     How  many  square  feet  in  1  sq.  yd.? 

3.  What  is  the  area  of  a  rectangle  12  in.  long 
and  1  in.  wide?   of  one  12  in.  by  12  in.? 

4.  Then  how  many  square  inches  in  1  sq.  ft.? 
Draw  a  square  foot  on  the  blackboard.      Draw  a 
square  inch. 

5.  How  many  feet  in  1  yd.?    Then  1  ft.  is  what 
part  of  1  yd.  ?     How  many  square  feet  in  1  sq.  yd.  ? 
Then  1  sq.  ft.  is  what  part  of  1  sq.  yd.? 

144  square  inches  =  1   square  foot  (sq.  ft.). 
9  square  feet  =  1  square  yard  (sq.  yd.). 

WRITTEN  EXERCISE 

1.  How  many  square  inches  in  25  sq.  ft.? 

2.  .How  many  square  feet  in  37  sq.  yd.? 

3.  How  many  9's  in  144?      How  many  times 
is  9  sq.  ft.  contained  in  144  sq.  ft.?     How  many 
square  yards  in  144  sq.  ft.? 

4.  How  many  square  yards  in  a  rectangle  30  yd. 
long  and  8  yd.  wide?    Draw  it,  using  \  in.  to  a  yard. 

5.  Find  the  area  of  a  rectangle  52  ft.  long,  32  ft. 
wide;   of  one  63  yd.  long,   58  yd.  wide;   of   one 
121  ft.  long,  16  ft.  wide. 


162 


PRIMARY   ARITHMETIC 


ORAL  EXERCISE 


1.  How  much    do  you   think  this  load  of  hay 
weighs?     How  many  pounds? 


2.  If  the  hay  weighs  1  ton  and  the  wagon  weighs 
800  lb.,  how  many  pounds  do  both  together  weigh? 

3.  Name  some  things  that  are  sold  by  the  ounce; 
by  the  pound ;  by  the  ton.     How  many  ounces  in 
a  pound?     How  many  pounds  in  a  ton? 

2OOO  pounds  =  1  ton  (T.). 

The  ton  is  used  in  weighing  substances  sold  in  heavy 
loads,  like  coal,  hay,  building  stone,  and  iron. 

There  is  another  kind  of  ton,  the  long  ton^  contain- 
ing 2240  lb.  It  is  not  much  used  except  in  some  mines. 


WRITTEN   EXERCISE 


1.  At  $9.75  a  ton,  what  will  17  T.  of  hay  cost? 

2.  At  $5.50  a  ton,  what  will  34  T.  of  coal  cost? 

3.  At  $36.60  for  6  tons,  what  will  1  T.  cost? 


REVIEW  163 

WRITTEN  EXERCISE 

1.  How  many  pounds  in  2  T.?    3  T.? 

2.  How  many  square  feet  in  19  sq.  yd.? 

3.  How  many  square  inches  in  17  sq.  ft.? 

Find  the  number  of  square  yards  in  the  rectangles 
in  Exs.  4~11 : 

4.  32  yd.  by  6  yd.  5.  27  yd.  by  9  ft. 
6.  27  ft.  by  36  ft.  7.  36  yd.  by  36  ft. 
8.  19  yd.  by  27  ft.             9.  54  ft.  by  32  yd. 

10.  29  yd.  by  18  ft.  11.  132  yd.  by  33  ft. 

Multiply  in  Exs.  12-30: 
12.  232  by  48.  13.  193  by  39.  14.  281  by  37. 
15.  298  by  32.  16.  341  by  27.  17.  341  by  17. 
18.  342  by  26.  19.  327  by  25.  20.  278  by  33. 
21.  462  by  19.  22.  496  by  18.  23.  419  by  17. 
24.  192  by  46.  25.  387  by  27.  26.  199  by  49. 
27.  $1.27  by  37.      28.  $3.29  by  19.  ' 
29.  $2.32  by  32.      30.  $1.92  by  36. 

Divide  in  Exs.  31-46 : 

31.  3426  by  6.  32.  3437  by  7.  33.  4328  by  8. 
34.  6237  by  9.  35.  1273  by  5,  36.  2681  by  4. 
37.  $12.75  by  5.       38.  $16.33  by  3. 
39.  $19.27  by  7.      40.  $15.26  by  6. 
41.  $125  by  $5.       42.  $724  by  $4. 
43.  $801  by  $9.       44.  $133  by  $7. 
45.  3900  by  52.       46.  2788  by  41. 


164 


PRIMARY   ARITHMETIC 


ORAL  EXERCISE 

1.  The  milkman  sells  the  milk  at  8  ct.  a  quart. 

How  much  is  this 
a  gallon? 

2.  The  dairy- 
man gets  only 
2^  ct.  a  quart  for 
the  milk.  How 
much  is  this  a 
gallon?  Why  is 
there  a  difference 
between  city  and 
country  prices? 

There  is  a  smaller 
measure  than  the  pint.     It  is  called  the  gill. 

4  gills  (gi.)  =  1  pint  (pt.). 
2  pints         =  1  quart  (qt.). 
4  quarts       =  1  gallon  (gal.). 

WRITTEN  EXERCISE 

1.  How  many  gills  in  7  pt.?   in27qt.?   injqt.? 

2.  How  many  pints  in  a  gallon  ?   in  f  gal.  ?   in 

fgalT 

3.  Th  s  milkman  delivers  200  qt.  of  milk  a  day 
at  8  ct.  a  quart,  and  50  pt.  of  crearn  at  40  ct.  a 
quart.     How  much  money  does  he  take  in  daily  ? 

4.  If  'he  200  qt.  of  milk  that  this  man  delivers 
cost  10  ct.  a  gallon,  how  much  did  the  dealer  gain 
on  it  with  which  to  pay  for  express  and  delivery  ? 


MEASURES  165 

ORAL  EXERCISE 

1.  How  many  men  go  to  the  fire  on  an  engine? 
How  many  with  the  hose  cart  ? 

How  many  with  both? 

2.  How  long  must  a  ladder 
be  to  reach 

the  third 
floor  above 
the  ground, 
the  lowest 
story  being 
18  ft.,  the 
next  10  ft., 
and  the  next  9  ft.,  allowing  5  ft.  extra  for  the  slant? 

WRITTEN  EXERCISE 

1.  How  long  must  an  extension   ladder  be  to 
reach  the  fifth  floor  above  the  ground,  the  lowest 
story  being  18 J  ft.,  the  next  12J  ft.,  and  the  rest 
10ft.  each,  allowing  5ft.  extra  for  the  slant? 

2.  The  engine    uses    two  lines   of  hose.     Each 
must  be  150  ft.  long  to  reach  the  building  and  the 
fifth  floor.     How  much  hose  must  there  be  in  all  ? 

3.  This  hose  weighs  130  Ib.  per  100ft.     How 
much  does  the  hose  mentioned  in  Ex.  2  weigh? 
It  is  in  50-ft.  lengths.     How  many  lengths? 

4.  The  engine  pumps  900  gal.  of  water  a  minute. 
How  much  can  it  pump  on  the  fire  in  an  hour? 


166 


PRIMARY   ARITHMETIC 


ORAL  EXERCISE 

1.  These  girls  have  found  tha^t  a  dessert  spoon 
holds    two    teaspoonfuls.      How    many    teaspoon- 
fills  do  they  need  for 
a    9-dessert-spoon 
recipe  ? 

2.  A  tablespoon 
holds  4   teaspoon- 
fuls.    How   many 
teaspoonfuls     do 
they  need  for  an  8- 
tablespoon  recipe? 

3.  A  small  teacup 
holds  1  gill.    How 

many  such  teacups  to  the  pint?     How  many  to 
the  quart? 

4.  A  pint  of  water  weighs   1  Ib.     How  much 
does  1  qt.  weigh?     How  much  does  1  gal.  weigh? 

WRITTEN  EXERCISE 

1.  If  45  drops  of  water  make  a  teaspoonful,  how 
many  drops  to  ^  of  a  teaspoonful?   to  f  ? 

2.  A  recipe  calls  for  If  teaspoonfuls  of  extract. 
This  is  1  teaspoonful  and  how  many  drops? 

3.  If  a  pint  of  water  weighs  1  Ib.,  how  many 
ounces  does  1  pt.  weigh?    1  qt.?   1  gi.? 

4.  A  common-sized  tumbler  holds  |  pt.  of  water. 
How  many  such  tumblers  to  a  quart?    How  many 
gills  to  a  tumbler? 


MEASURES  167 

ORAL  EXERCISE 

1.  How  many  seconds  make  a  minute? 

2.  How  many  minutes  make  an  hour? 

3.  Close  your  eyes,  and  raise  your  hand  when 
you  think  one  minute  has  passed. 

4.  How  many  hours  make  a  day?     (This  means 
a  day  and  night  together.) 

5.  Tell   the   names   of   the   months   that   have 
thirty  days  each.     Of  the  others,  name  one  that 
does  not  have  thirty-one  days. 

6.  Do  you  know  how  many  days  there  are  in  a 
year?    Every  four  years  there  is  a  leap  year.    How 
many  days  then? 

You  have  learned  (page  63)  the  table  of  time,  except 
the  following: 

365  days  =  1  year  (yr.),  except  the  leap  y^ar. 
3O  or  31  days  =  1  month  (mo»),  except  February. 
12  months  =  1  year. 

In  leap  years  February  has  29  days,  and  the  year  has 
366  days. 

WRITTEN  EXERCISE 

1.  How   many  hours  do   you  spend  in   school 
every  day  ?     How  many  minutes  is  this  ? 

2.  How   many   hours  do  you   spend  in   school 
every  week?   every  4  wk.?   every  36  wk.? 

3.  There  are  5  school  days  in  a  week  and  36 
school  weeks  in  a  year.     How  many  school  days 
are  there  in  a  year  ? 


168  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  If  you  were  to  measure  the  length  of  your 
state,  would  you  measure  by  miles  or  by  feet? 

2.  If  you  were  to  measure  your  schoolroom,  would 
you  measure  by  miles,  or  by  feet,  or  by  inches? 

3.  If  you  were  to  measure  your  finger,  would 
you  measure  by  yards,  or  by  feet,  or  by  inches? 

4.  If  asked  your  age,  would  you  answer  in  years 
or  in  weeks  ?     If  asked  how  long  before  you  would 
go  home  to-day,  how  would  you  answer? 

When  we  measure  anything  by  feet  we  call  the  foot 
the  unit  of  measure.  So  if  we  measure  weight  by  the 
pound,  the  pound  is  the  unit  of  measure. 

In  measuring  great  lengths  we  use  the  mile  as  the 
unit.  For  lengths  less  than  1  mi.  we  often  use  yards 
or  feet.  For  small  distances  we  often  use  the  inch. 
For  time  we  use  the  second,  minute,  hour,  week,  and 
so  on. 

MEASURING 

1.  Measure  the  length  of  the  room,  using  as  the 
unit  1  ft.;  also  1  yd. 

2.  Measure  the  length  of  the  desk,  using  as  the 
unit  1  ft.;  also  1  in. 

3.  Measure  the  height  of  the  desk,  using  as  the 
unit  1  ft.;  also  1  in. 

4.  Imagine  a  square  36  in.  on  a  side.    Measure  its 
area,  using  1  sq.  ft.  as  the  unit ;  also  using  1  sq.  yd. 
Draw  a  picture  on  a  scale  of  1  in.  to  1  ft. 


MEASURES  169 

ORAL  EXERCISE 

Tell  the  answers  rapidly : 

1.  241  +  102.  2.  $241 +  $201. 

3.  120  ft.  +  220  ft.  4.  125  mi.  +  75  mi. 

5.  $450 -$150.  6.  47ibu.-ibu. 

7.  48f  bu. -Jbu.  8.  101  sq.ft.  -£  sq.  ft. 

9.  9  times  800  ft.  .10.  9  times  71  mi. 

11.  8  times  $21.  12.  5  times  $200. 

13.  72  ft.  *  8.  14.  $250  -  5. 

15.  $40  -  8.  16.  350  ft.  4-  7. 

17.  819  ft.  -  9.  18.  |  of  488  yd. 

WRITTEN  EXERCISE 

The  toad  is  one  of  man's  best  friends.    One  toad  will 
keep  a  garden  of  800  sq.  ft.  free  from  harmful  insects. 

1.  At  this  rate,  how  many  toads  would  protect 
from  insects  a  garden   80  ft. 

wide  and  100  ft.  long? 

2.  The  eggs  of  4  toads  were 
counted  and  found  to  be  7547, 
11,540,7927,  and  9536.    How 
many  were  there  in  all  ? 

3.  If  one  out  of  50  hatched,  how  many  hatched? 
(Divide  all  by  50.)     If  715  of  these  were  destroyed 
by  other  animals,  how  many  survived? 

4.  If  each  of  these   survivors   destroys  insects 
that  would  cause  $10  worth  of  damage,  how  much 
are  they  all  worth  to  a  village  ? 


170 


PRIMARY    ARITHMETIC 


WRITTEN   EXERCISE 


Add: 

1 

.  2634 

2.  804 

3.  | 

;82 

.75 

4.  $91. 

75 

296 

1427 

31 

.42 

66. 

73 

1472 

3600 

68 

.93 

8. 

49 

2108 

584 

4 

.67 

4. 

81 

436 

796 

5 

.21 

16. 

00 

Subtract  : 

5 

.  $632.48 
429.53 

6. 

$832.49 
59.81 

7. 

$293.50 
67.98 

Multiply: 
8.  743  by  26.       9.  674  by  57. 

Divide: 
11.  1728  by  12.      12.  832  by  32. 

Add: 
14.  27|  15.  16^         16.  21| 


Subtract: 
18.  35f 
12* 


19.  42J 


20.  31| 


10.  248  by  83. 
13.  5125by41. 


17.  23|- 
19f 


21.  91| 


22.  Find  J  of  720 ;  also  J,  f ,  \,  and  f  of  720. 

23.  Find  i,  |,  |,  |,  i,  and  |  of  1440. 

24.  Find  |  of  165,  222,  471,  522. 

25.  Find  |  of  275,  340,  785,  4600.  ' 

26.  Find  f  of  640,  760,  112,  3240. 

27.  Find  |  of  420,  675,  825,  4305. 


CHAPTER  IV 

I.    NUMBERS  TO  100,000.     SPECIAL  ATTENTION 
TO   MULTIPLICATION  AND   DIVISION 

COUNTING   REVIEWED 

ORAL   EXERCISE 

1.  Count  by  2's  from  2  to  24.     Give  tlie  multi- 
plication table  of  2's  to  12  times  2. 

2.  Count  by  3's  from  3  to  36.     Give  the  multi- 
plication table  of  3's  to  12  times  3. 

3.  In  the  same  way  count  by 

4's  to  48,  giving  the  multiplication  table  to  12  times  4  ; 

5's  to  60,  "  «  "  "  "  "  "     5 ; 

6's  to  72,  "  "  "  "  "  "  "      6  ; 

7's  to  84,  «  «  "  "  "  "  "      7 ; 

8's  to  96,  "  «  "  "  «  «  "'     8 ; 

9's  to  108,  "  "  "  "  "  "  "  9 ; 

10's  to  120,  "  "  "  "  "  "  "  10; 

ll's  to  132,  "  "  "  u  "  "  "  11 ; 

12's  to  144,  "  «  «  "  "  «'  "  12. 

WRITTEN   EXERCISE 

Write  the  multiplication   table    from  1  x  1  to 
12  x  12. 

171 


172  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  Count  by  10's  from  10  to  100. 

2.  Count  by  100's  from  100  to  1000. 

3.  Count  by  1000's  from  1000  to  10,000. 

4.  Count  by  10,000's  from  10,000  to  100,000. 

In  the  number  23,546  a  comma  (,),  sometimes  called 
a  separatrix  when  used  like  this,  is  written  between  the 
thousands  and  hundreds.  This  makes  it  easier  to  read 
the  number. 

In  the  number  23,546 

the  6  occupies  units'  place, 
"    4        "         tens'  place, 
"    5        "         hundreds'  place, 
"    3        "         thousands'  place, 
"    2        "         ten  thousands'  place, 
and  in  the  number  100,000,  the   1  occupies  hundred 
thousands'  place. 

WRITTEN   EXERCISE 

1. -Write  the  numbers:  forty  thousand,  four 
hundred  four;  seventy  thousand,  seven  hundred 
forty-seven;  sixty-four  thousand,  seven  hundred 
eighty-eight;  ninety-eight  thousand,  seven  hundred 
sixty-five ;  fifty  thousand,  five ;  sixty-six  thousand, 
six  hundred  sixty-six ;  ten  thousand,  ten. 

2.  Write  in  words  the  numbers  :   1234;  12,345; 
34,567;  45,678;  56,789. 

3.  Write  in  words  the  numbers  :  64,742;  73,498; 
60,006;  75,075;  12,345;. 92,846;  10,001. 


UNITED   STATES   MONEY  173 

UNITED   STATES   MONEY 

ORAL   EXERCISE 

Read  the  amounts  in  Exs.  1-9: 
1.  .$4.75.  2.  $26.50.          3.  $92.05. 

4.   $10.10.  5.   $0.621.  6.   $2.121 

7.  $3.33i.  8.  $3475.75.      9.  $11,245.50. 

The  teacher  should  write  all  the  numbers  in  Exs.  10-18  on  the 
blackboard,  or  refer  to  the  book. 

Add  the  numbers  in  Exs.  10-15: 
10.  $250.25  11.  $475.15          12.  $275.62 

325.10  102.12  23.00 

13.  $407.75  14.  $0.75  15.     $0.25 

92.00  0.13  32..7S 

Subtract  the  numbers  in  Exs.  16—18: 
16.  $425.75  17.  $350.50          18.  $825.50 

110.25  120.00  125.25 


WRITTEN   EXERCISE 

Multiply  in  Exs.  1-4: 

1.  $233          2.  |322          3.  $505  4.  $1601 

32                    43                    64  19 

Divide  the  following : 

5.  $9676-41.      6.  $9288-72.      7.  $9936-92. 

8.  $7128-81.      9.  $9579-31.    10.  $8569  +  41. 


174  PRIMARY   ARITHMETIC 

ADDITION 
ORAL  EXERCISE 


Add: 

1.  20 

28 

28 

28 

38 

48 

30 

30 

5 

35 

35 

35 

2.  40          44         44         44         45         45 
60          60         _7         67         67         69 

3.  70          73         73         73         74         74 

90          90         _8          98          98          99 

You  see  from  the  above  examples  that  it  is  not  difficult 
to  add  at  sight  two  numbers  of  two  figures  each.  67 
Thus,  add  67  and  58,  and  say:  "58,  65  (that  is,  58 
58  +  7),  125  (that  is,  65  +  60,  because  6  +  6  =  12)."  125 

4.  97          73         81         73         66         75 

68          49          96          37          48          89 

5.  Add,  if  possible  without  writing  the  numbers  : 
147        246        349        683        532        829 

32          64         72          48          96          53 

6.  If  you  buy  38  ct.  worth  of  cloth  and  23  ct. 
worth  of  ribbon,  how  much  do  you  pay  ? 

7.  If  you  weigh  53  Ib.  and  Cora  weighs  48  lb.? 
how  much  do  you  both  weigh  ? 

8.  If  a  farmer  buys  one  cow  for  $38  and  another 
for  $43,  how  much  do  both  cost? 


ADDITION  175 


WRITTEN  EXERCISE 

The  pupils  should  add  rapidly  from  the  lowest  number  upwards, 
and  check  by  adding  from  the  top  downwards.  They  should  see 
how  many  of  the  following  they  can  add  and  check  in  five  min- 
utes, taking  them  in  order. 


1. 

2. 

3. 

4. 

5. 

$482.75 
122.30 

$181.23 
62.49 

$822.72 
406.91 

$32.98 
149.72 

$909.92 
98.00 

42.65 

426.32 

329.92 

683.09 

6.49 

308.70 

43.71 

67.42 

9.89 

.93 

6. 

7. 

8. 

9. 

10. 

$498.92 
92.68 

$32.99 
841.00 

$234.27 
26.42 

$0.35 
21.62 

$298.38 
23.42 

34.41 

0.68 

982.00 

342.71 

671.82 

9.00 

32.97 

4.39 

459.00 

84.96 

11. 

12. 

13. 

14. 

15. 

$293.48 
64.79 

$429.30 
62.41 

$298.75 
92.30 

$293.49 
98.71 

$674.00 
82.96 

392.60 

67.92 

68.70 

634.00 

3.09 

34.48 

38.00 

491.63 

82.98 

842.00 

27.62 

526.00 

90.89 

99.81 

891.75 

16. 

17. 

18. 

19. 

20. 

$342,42 
27.92 

$426.26 
290.30 

$329.30 
49.30 

$298.75 
32.78 

$129.30 
472.63 

31.82 

320.30 

67.29 

62.96 

87.96 

61.49 

42.87 

9.37 

34.21 

54.98 

827.30 

67.42 

402.72 

293.48 

209.00 

82 

82 

82 

82 

30 

_7 

37 

47 

46 

46 

46 

46 

20 

9 

29 

27 

176  PRIMARY   ARITHMETIC 

SUBTRACTION 

ORAL    EXERCISE 

1.  Subtract:       95  95  95  95 

60  J>  66  86 

2.  Subtract: 

3.  Subtract: 


You  see  from  the  above  examples  that  it  is  not  diffi- 
cult to  subtract  one  number  of  two  figures  from  45 
another  one.  Thus,  to  subtract  29  from  46,  find  29 
46  -  9  -  37,  and  37  -  20  =  17.  17 

4.  Subtract:       52  73  67  81 

36  48  39  35 

5.  From  52  subtract  15;   from  the  result  sub- 
tract 19. 

6.  If  you  buy  33  ct.  worth  of  groceries  and  give 
the  grocer  half  a  dollar,  how  much  change  should 
you  receive  ? 

7.  If  you  buy  40  ct.  worth  of  candy  and  18  ct. 
worth  of  cookies,  how  much  change  should  you 
receive  for  75  ct.? 

8.  If  you  buy  90  ct.  worth  of  meat  and  37  ct. 
worth  of  fish,  and  give  the  dealer  $1.50,  how  much 
change  should  you  receive  ? 


SUBTRACTION  177 
WRITTEN   EXERCISE 

See  how  long  it  takes  you  to  perform  these  sub- 
tractions.    You  should  have  no  mistakes  when  you 
finish  the  ivork,  because  you  should  check  each  result. 
1.                  2.                   3.                  4.  5. 

$281.42  $691.75  $298.30  $427.20  $532.60 

135.02   208.02   107.60   109.32  237.62 


6. 

$532.65 
206.39 

7. 
$281.92 
192.60 

8. 

$409.72 
286.58 

9. 

$672.35 
148.39 

10. 

$491.63 
269.75 

11. 

$426.32 
126.49 

12. 

$298.91 
129.92 

13. 

$427.32 
334.48 

14. 

$681.48 
496.12 

15. 

$429.39 
330.26 

16. 

$929.32 
830.40 

17. 

$807.21 
720.32 

18. 

$600.00 

48.75 

19. 

$505.02 
60.80 

20. 

$829.09 
298.90 

21. 

$400.00 
39.75 

22. 

$209.00 
60.40 

23. 

$300.40 
29.09 

24. 

$402.70 
80.79 

25. 

$620.02 
69.91 

26. 

$800.25 
549.25 

27. 

$402.33 
60.48 

28. 

$627.03 
39.72 

29. 

$481.02 
99.80 

30. 

$302.04 
.40.60 

31. 

$127.49 
49.89 

32. 

$292.08 
98.75 

33. 

$600.05 
62.70 

34. 

$481.27 
90.39 

35. 

$926.30 
48.75 

178  PRIMARY   ARITHMETIC 

WRITTEN  EXERCISE 

1.  I  know  a  village  in  which  there  are  2473 
men,  2587  women,  and  3575  boys  and  girls.    How 
many  are  there  in  all? 

2.  In  one  school  in  the  village  there  are  127 
girls,  and  the  number  of  boys  is  19  less.     How 
many  pupils  are  there  in  the  school? 

3.  The  school  ground  is  100  ft.  along  the  street 
and  165  ft.  deep.     The  trustees  wish  to  put  a  new 
fence  around  the  lot.    How  many  feet  of  fence  are 
needed? 

4.  After  school  on  Monday  one  of  the  boys  sold 
32  papers,  and  during  the  next  five  days  he  sold 
27,  19,   31,  41,  and  23.     How  many  did  he  sell 
during  the  week? 

5.  If  the  attendance  at  the  school  this  year  is 
235,  and  if  it  was  27  less  last  year,  and  19  less 
than  that  the  year  before,  how  much  was  it  year 
before  last  ? 

6.  The  expenses  of  the  school  this  year  are  as 
follows:  teachers,   $2325;  fuel,  $297.45;  janitor, 
$425;  insurance,  $32;  books,  maps,  and  supplies, 
$355.70 ;    repairs,     $81.55 ;    shrubbery    for    the 
grounds,    $23.75.       How   much   were    the    total 
expenses? 

7.  Last   year  the  expenses  of  the  school  were 
$263.20  less  than   this  year.      How  much  were 
they  then? 


MULTIPLIC  ATION  179 

MULTIPLICATION 

ORAL  EXERCISE 

The  tables  should  be  reviewed  continually,  not  only  as  tables, 
but  more  frequently  by  asking  for  various  products,  as  6x7, 
9x3,  and  4x8. 

1.  Multiply  7  by  2,  10  by  2,  17  by  2,  18  by  2, 
19  by  2. 

2.  Multiply  6  by  3,  10  by  3,  16  by  3,  15  by  3, 
14  by  3. 

3.  Multiply  12  by  4,  12  by  3,  11  by  4,  11  by  3,- 
12  by  2. 

4.  State  two  numbers  which  multiplied  together 
make  50;  49;  48;  46;  45;  44;  42;  39;  38;  36; 
35;  34;  33;  32. 

5.  State  all  the  pairs  of  numbers  which  multi- 
plied together  make  50 ;  45 ;  44 ;  36. 

WRITTEN  EXERCISE 

1.  If  £  of  a  yard  of  silk  costs  19  ct.,  what  will 
1  yd.  cost  at  the  same  rate? 

2.  If  |  of  a  yard  of  velvet  costs  72  ct.,  what  will 
I  yd.  cost?   |  yd.,  or  1  yd.? 

3.  If  |  of  a  yard  of  ribbon  costs  64  ct.,  what  will 
|  yd.  cost?     Then  what  will  1  yd.  cost? 

4.  If  |   of  a  yard   of  furniture  tapestry  costs 
$1.95,  what  is  the  rate  per  yard? 

5.  If  35  yd.  of  silk  velvet  costs  $70,  how  much 
will  12  yd.  cost? 


180  PRIMARY   ARITHMETIC 

WRITTEN  EXERCISE 

In  these  examples  in  multiplication  see  how  large 
a  score  you  can  make  in  five  •  minutes,  counting 
every  correct  result  7,  and  subtracting  2  for  every 
incorrect  result. 

1.  $293.50  2.  $482.60  3.  $981.75  4.  $371.72 
5    7    6 8 

5.  $309.72  6.  $402.03  7.  $625.72  8.  $829.30 
9    12        11    13 

9.  $575.25  10.  $609.72  11.  $572.30  12.  $986.75 
15       18    21    25 

13.  $421.30  14.  $531.92  15.  $683.40  16.  $532.20 
23    32    35    45 

17.  $681.40  18.  $700.09  19.  $682.02  20.  $409.60 
52    41       53    55 

You  have  learned  how  to  multiply  by  a  two-figure 
number.  It  is  nearly  as  easy  to  multiply  by  a  three- 
figure  number.  For  example,  multiply  348  by  234. 

This  shows  the  full  work:  But  we  write  only  this: 

348  348 

234  234 

1392  product  by     4  1392 

10440         «       "    30  1044 

69600         "       "  200  696 

81432         "       "  234  81432 


MULTIPLICATION  181 

WRITTEN  EXERCISE 

Multiply : 

1.  $340          2.  $409          3.  $629          4.  $4987 
175  243  121  46 

5.  $61.72       6.  428            7.  329             8.  $14.75 
54  231  246  125 

9.  $527.30   10.  $426.30  11.  $462.75   12.  $329.82 
64         68         39 98 

13.  $472.96  14.  $309.87  15.  $481.20   16.  $502.75 
_ 89 72        64         69 

17.  $681.39   18.  $17.42     19.  $21.50     20.  $491.76 
JT2  146  371  81 

21.  At  $85  an  acre,  how  much  are  164  acres  of 
land  worth? 

22.  At  $37.50  a  head,  how  much  are  38  head  of 
cattle  worth? 

23.  At  $36  a  dozen  for  milk  cans,  how  much 
will  a  farmer  have  to  pay  for  14  cans? 

24.  If  the  school  buys  15  dictionaries  at  $6.75 
each,  how  much  will  it  pay  for  all? 

25.  If  a  dealer  pays  $3.84  for  a  dozen  arithme- 
tics, how  much  will  144  cost? 

26.  A  man  buys  4  head  of  cattle  for  $168,  and 
adds  them  to  his  dairy.     He  then  sells  off  13  at 
this  same  price  apiece.     What  does  he  receive? 


182  PRIMARY   ARITHMETIC 

DIVISION 

You  have  learned  how  to  divide  by  numbers  of  one 
figure,  and  by  two-figure  numbers  ending  in  0,  1,  or  2. 
We  will  now  divide  by  other  two-figure  numbers.  For 
example,  divide  2701  by  73. 

We   see   that   2000  -^73  -no   thousands,  37 

2700  -*-  73  =  no    hundreds,    but    2700  +  73     73)2701 
=  3  tens,  with  511  still  to  be  divided.     We          219 
then  see  that  511  -=-73  =  7.     Therefore,  the  511 

quotient  is  37. 

A  satisfactory  understanding  of  a  process  like  this  comes 
only  from  blackboard  work  before  the  class,  followed  by  plenty 
of  drill. 

To  check  the  result,  we  have  found  that  the  quotient 
multiplied  by  the  divisor  equals  the  dividend.  Here, 
73  times  37  equals  2701. 


WRITTEN  EXERCISE 

1.  725-25.      2.  5143-37.      3.  9990-45. 
4.  3219-29.     5.  3465-35.       6.  3108-14. 

7.  If  a  farmer  pays  $1935  for  43  head  of  cattle, 
how  much  does  he  pay  a  head  ? 

8.  An  agent  sells  23  sewing  machines  for  $483. 
How  much  does  he  receive  on  an  average  for  each? 

9.  The  school  attendance  for  23  days  in  our  room 
was  805.    What  was  the  average  daily  attendance? 

10.  A  city  dealer  bought  25  children's  bicycles 
for  $275.     How  much  did  they  cost  apiece? 


DIVISION  183 

Required  to  divide  $198.32  by  74. 

This  shows  the  full  work:          But  we  write  only  this: 

$2.68  $2.68 

74)$198.32  74)  $198.32 

148      -  74  times  $2  148 

50.32  still  to  be  divided  503 

44.40  -  74  times  $0.60  444 


5.92  still  to  be  divided  592 

5.92  =  74  times  $0.08  592 

Because  74  is  not  contained  in  1,  $100  —  74  =  no 
hundreds  of  dollars.  Because  74  is  not  contained  in  19, 
$190  —  74  =  no  tens  of  dollars.  Because  19  -5-  7  =  more 
than  2  but  less  than  3,  we  see  that  $198  -*-  74  =  $2,  with 
$50.32  still  to  be  divided.  $50.32  -s-  74  =  $0.60,  with 
$5.92  still  to  be  divided.  $5.92  -*-  74  =  $0.08.  There- 
fore, the  quotient  is  $2.68. 

WRITTEN  EXERCISE 

1.  $181.44-56.  2.  $110.45-47. 

3.  $188.79-87.  4.  $85.47-77. 

5.  $1602.54-58.  6.  $160.16-44. 

7.  A  dealer  paid  $32.40  for  2  doz.  sleds.     How 
much  did  they  cost  apiece? 

8.  A  clothing  dealer  paid  $230.40  for  32  boys' 
suits.     How  much  did  he  pay  per  suit? 

9.  A  merchant  paid  $34.56  for  4  doz.  boys'  hats. 
How  much  did  they  cost  apiece? 

10.  If  6  doz.  dolls  cost  a  dealer  $27.36,  how 
much  did  they  cost  apiece? 


184  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  We  say  that  21  —  4  =  5,  and  1  remainder  ;    or 
that   2  1-5-4  =  5^-.     In   what   two   ways    can   you 
express  the  result  of  dividing  29  by  6? 

2.  In  the  same  way,  give  the  results  of 
35-8,  45-6,  81-8-8,  74-9,  48-5,  60-8. 

3.  Show    from    this    line    that 
T22-  =  J,  and  that  £  =  J. 
4.  To  what    simpler   fractions    are  T42,   T62?    12? 
T92,  and  j|  equal? 

',       5.  Show    from    this    line    that 
YO  =  ^-.    To  what  simpler  fractions 


1 1 1 '  I  • '  1 ' 


are  10  >  T5o  9  TO  j  and  TO 

6.  Divide:    10)70  +  5  -10)85    12)60  +  6    12)^64 

You  have  seen  (page  124)  that  we  may  have  remain- 
ders, and  that  these  give  fractions  in  the  quotients. 
For  example,  68  -f-  12  =  5^  =  5f  .         12)68 

~ 


WRITTEN  EXERCISE 


1.90-12. 
4.100-12. 
7.150-12. 
10.672-10. 
13.723-11. 

2.70-12. 
5.114-12. 
8.180-12. 
11.938-10. 
14.429-H. 

3.89-12. 
6.126-12. 
9.455-10. 
12.895-10. 
15.892-11. 

16.741-11.  17.  $25.26-12.  18.  $42.66-12. 
19.  $58.11-12.  20.  $39.64-12.  21.  $342.70-12. 
22.  $606.06-12.  23.  $493.30-12..  24.  $829.24^12. 


DIVISION  185 

In  the  division  of  34,943  by  82,  the  first  dividend  used 
is  349  (hundreds).    It  426^ 

is  called  the  first  par-     82)34943'  *    349  -  first  partial 
tial  dividend.  32800  dividend 

The   second    divi-  214  =  second  partial 

dend    used     is     214  164  dividend 

(tens).     It   is    called  503  =  third  partial 

the      second     partial  492  dividend 

dividend.  n  remainder 

503  is  the  third  partial  dividend. 

The  first  figure  in  the  quotient,  4,  was   found  by 
seeing  that  34  -r-  8  —  nearly  4. 

This  operation  in  which   the    partial  dividends    are 
written  out  is  called  long  division. 

When  the  partial  dividends  are  not  written     6)246 
out,  the  operation  is  called  short  division.  41 

You  have  found  (page  148)  that  0  may  be  a 
figure  in  the  quotient.  This  does  not  change 
the  work,  as  you  will  see  in  this  case  of 
12,464 -Ml. 

To  check  the  result,  41  x  304  -  12,464. 


WRITTEN  EXERCISE 

1.  2121  +  21.      2.  5304  +  52.      3.  10,556  -  52. 

4.  8526  -  42.      5.  6510  *  62.      6.  72,981  +  81. 

7.  2464  +  61.      8.  7536  *•  71.      9.  19,099  +  21. 

10.  8362  -  92.    11.  9-384  -  92.     12.  73,895  +  82. 

13.  A  dealer  sends  to  the  publisher  an  order  for 

41  arithmetics.     The  bill  is  $12.71.     How  much 

does  each  book  cost? 


186  PRIMARY  ARITHMETIC 

ORAL  EXERCISE 

1.  Divide  :  12)1200  +  120  +  12,  which  is  the  same 
as  12)1332. 

2.  Divide:  11 )  1100  +  440  +  77,  which  is  the  same 
as  11)1617. 

Teachers  who  find  classes  prepared  for  using  short  division  in 
dividing  by  11  and  12  may  use  the  following. 

While  you  have  learned  how  to  divide  by  11  and  by 
12    by   long  division,   you    see   that   you 
can  use  short  division,  as  in  the  case  of 
8917-12. 

You  may  think  :  "  I  do  not  know  the  quotient  of 
8917-12,  but  I  know  that  8400-12  =  700,  leaving 
517  to  be  divided.  I  do  not  know  the  quotient  of 
517-12,  but  I  know  that  480-12  =  40,  leaving  37 
to  be  divided.  37  - 12  =  3^.  Therefore,  the  quotient 
is  743Ty 

In  dividing  by  £,  3,  h  and  so  on  to  12,  you  should 
use  short  division. 

WRITTEN  EXERCISE 

1.  2223-11.        2.  1608-11.       3.  1224-12. 
4.  2473-12.       5.  7295-12.       6.  1617-11. 

7.  At  $42.00  a  dozen,  how  much  will  a  school 
desk  like  yours  cost?    How  much  will  8  cost? 

8.  At    $186   a  dozen  suits,  how   much   will  a 
dealer  have  to  pay  per  suit  for  clothing? 

9.  At  $90  a  dozen,  how  much  must  a  jeweler 
pay  for  3  clocks  ? 


DIVISION  187 

ORAL   EXERCISE 

1.  Divide:    400-10,    $4-10. 

2.  Divide  :    60  -  20,  60  -  30,  600  -  30. 

3.  Divide  :    900  -  30,    9000  •*•  30,    900  ct.  -  30, 
$9-30. 

4.  What  is  the  short  way  of  dividing  a  number 
that  ends  in  0  by  10?   by  20?   by  30?   by  40? 

5.  By  what   fraction    do  you   indicate  |  of  2? 
of  4?   of  6?   |  of  8  =  If?  ' 

6.  75-10  =  7TV  =  7f  ?   85  -10  equals  how  many? 

You  have  found  (page  144)  that  there  is  a  short  way 
of  dividing  by  10  or  by  any  number  of  10's. 

10)7260  20)7260  30)7270 

726  363 


If  the  dividend  does  not  end  in  0,  you  found  by 
Ex.  6,  above,  that  you  could  still  use  this  short  way. 
For  example,  divide  7267  by  10,  20,  and  30. 

10)  726  1  7   '  20)726|7  30)726|7 

726TV  363^  242¥V 

WRITTEN  EXERCISE 

Divide.,  using  short  division: 

1.  1720  -  20.       2.  $2350  -  20.     3.  52,350-50. 

4.  31,200-30.     5.  23,240-20.      6.  21,350-50. 

7.  405,370-90.  8.  124,810-80.  9.  100,100-70. 
10.  314,610-30.  11.  124,360-40.  12.  402,360-60, 
13.  $48.27  -  4.  14.  $29.63  -  2.  15.  $35.73  -  4. 
16.  $217.63-5.  17.  $402.01-5.  18.  $222.22-8. 


188  PRIMARY   ARITHMETIC 

In  much  the  same  way  as  on  page  185,  we  may 
divide  by  three-figure  numbers.  For  example,  divide 
12,525  by  501. 

This  shows  the  full  work:         But  we  write  only  this: 

25  25 

501  )12525  501 )12525 

10020  =  501  x  20  1002 

2505  still  to  be  divided  2505 

2505  =  501  x  5  2505 

Since  the  product  of  25  and  501  is  12,525,  the  work 
is  right. 

WRITTEN  EXERCISE 

1.  $8687  *  $512.          2.  $249.83  +  301. 
3.  $33,732-912.         4.  $397.39-811. 
5.  $511.11-631.         6.  $2269.47-707. 
7.  $467.25  -  623.         8.  47,595  ft.  -  501  ft. 
9.  A   man   bought    211    sheep    for   $1529.75. 
How  much  was  this  a  head  ? 

10.  He  sold   these   sheep  for   $1550.85.     How 
much  did  he  receive  a  head? 

11.  With  the  money  received  from  the  sheep  he 
purchased  cattle  at  $31  a  head.    How  many  could 
he  buy,  and  how  much  had  he  left  after  buying  as 
many  as  he  could  ? 

12.  If  he  had  taken  the  $1550.85  and  bought 
15  horses,  how  much  would  have  been  the  average 
price? 

13.  If  he  had  taken   $1032.75  of  his   money, 
and  with  it  bought  153  sheep,  how  rniich  wpuld 
he  have  paid  a  head? 


DIVISION  189 

Sometimes  a  mistake  is  made  in  making  the  quotient 
figure  too  large.  For  example,  divide  4375  by  175. 

Because  4-^-1=4,  it  might  at  first  be  9_ 

thought  that  437  -s-  175  -  nearly  4.  But  ,-^5- 

this  cannot  be  right,  for  175  is  nearly  200, 


and  437  -*-  200  is  only  a  little  over  2.  -— 

If  the  quotient  is  taken  too  large,  the  par- 

tial product  will  be  greater  than  the  dividend. 

If  the  quotient  is  taken  too  small,  the  remainder  will 

be  greater  than  the  divisor. 

WRITTEN  EXERCISE 

1.  $971.25-111.  2.  $1611.42-321. 

3.  $10,593-107.  4.  $343.68-537. 

5.  $139.30-870.  6.  $961.88-346. 

7.  $173.13-199.  8.  $321.30-306. 

9.  $142.74-234.  10.  $97.01-109. 

11.  $223.11-111.  12.  $1406.25-225. 

13.  If  98  machines  cost  $3456.46,  what  is  the 
cost  of  each? 

14.  If  175  tons  of  hay  cost  $1837.50,  what  is 
the  cost  per  ton? 

15.  If  121  yd.  of  carpet  cost  $78.65,  how  much 
does  it  cost  per  yard  ? 

16.  A  cement  walk  81  ft.  long  and  5  ft.  wide 
cost   $141.75.     How  much  did  it  cost  per  square 
foot? 

17.  A   carpet   dealer   has  on  hand    221  yd.   of 
carpet  that  cost  him  $106.08.     At  this  rate,  how 
much  did  53  yd.  cost  him? 


190  PRIMARY   ARITHMETIC 

FRACTIONS 
ORAL  EXERCISE 

1.  First  think  |  of  each  of  these  numbers,  and 
then  state  f  of  each:  9,  6,  12,  3,  21,  30. 

2.  First  think  ^  of  each  of  these  numbers,  and 
then  state  f  of  each:  32,  40,  12,  24,  20,  28. 

3.  First  think  |  of  each  of  these  numbers,  and 
then  state  f,  or  f ,  or  |   of  each,  as  the  teacher 
directs:  20,  45,  30,  5,  50,  15,  40,  25,  10,  35. 

4.  Think  ^  of  each  of  these  numbers,  and  then 
state  |  of  each  :   48,  24,  36,  42,  18,  12,  36,  54,  60. 

5.  Think  |  of  each  of  these  numbers,  and  then 
state  |,  or  f,  or  |,  of  each,  as  the  teacher  directs: 
64,  32,'  24,  16,  40,  8,  72,  48,  56,  80. 

6.  State  rapidly  i,  J,  £,  1,  f,  f,  f,  of  12;   also 
of  24 ;  also  of  36. 

WRITTEN  EXERCISE 

1.  From  f  of  712  subtract  f  of  928. 

2.  From  }  of  576  subtract  f  of  216. 

3.  Add  I  of  288,  f  of  288,  and  f  of  714. 

4.  Add  ^  of  1104,  |  of  1104,  and  |  of  1104. 

5.  Add  i  of  $29.64,  £  of  $73.80,  £  of  $174.48, 
and  |  of  $203.60. 

6.  How  much  more  is  |  of  $2640  than  \  of  the 
same  amount? 

7.  How  much  less  is  \  of  $26.40  than  |  of  the 
same  amount? 


REVIEW  191 


ORAL  EXERCISE 

1,  A  farmer  has    25  sheep   in  one  lot,  25  in 
another,  and  10  in  a  third.     How  many  has  he? 


2.  He  expects  9  Ib.  of  wool  from  each  in  the 
spring.     How  many  pounds  will  he  have  in  all? 

3.  If  half  of  the  flock  of  sheep  are  worth  $6  a 
head,  what  is  the  value  of  this  half  ? 

WRITTEN  EXERCISE 

1.  One  quarter  of   the  flock  cost  him  $6.20  a 
head.     How  much  did  he  pay  for  this  lot? 

2.  If  half  of  his  sheep  cost  $6  a  head,  a  quarter 
$5  a  head,  and  the  rest  of  them  $6.20  a  head, 
how  much  did  they  all  cost  ? 

3.  Taking  this  total  cost,  and  knowing  that  there 
were  60  in  all,  find  the  average  price  per  head. 

4.  He  averaged  9|  Ib.  of  wool  from  each  sheep, 
and   sold  it  for  44  ct.   a  pound.    What  was  the 
wool  of  the  60  sheep  worth  at  this  rate? 

5.  If  it  cost  this  farmer  40  ct.  a  hundred  pounds 
to  get  the  wool  to  market,  how  much  did  it  cost  to 
get  all  of  the  wool  there? 


192  PRIMARY    ARITHMETIC 


ORAL   EXERCISE 


1.  How  much  is  \  of  24  ?  £  of  30  ?  their  sum? 

2.  How  much  is  J-  of  20  ?  £  of  24  ?  their  sum? 

3.  How  much  is  %  of  30,  minus  J  of  16? 

4.  How  much  is  ^  of  30,  minus  ^  of  20? 


5.  How  many  halves  in  1  ?  inl^?  in  2  ?  Express 
|  as  a  whole  number  and  a  fraction.  Express  |  as 
a  whole  number. 


6.  How  many  thirds  in  1?  in  1|?  in  If  ?  in  2? 
Express  f  and  f  as  whole  numbers  and  fractions. 
Express  f  as  a  whole  number. 


WRITTEN   EXERCISE 


1.  |  of  36  +  J  of  20.  2.  I  of  36  -  i  of  12. 

3.  |  of  32  +|  of  30.  4.  |  of  32  -  J  of  24. 

5.  24  +  |  of  24,  or  1£  times  24. 

6.  36  +  §  of  36,  or  If  times  36. 

7.  50  +  £  of  50,  or  f  of  50. 

8.  |  of  15;  of  21;  of  33;  of  36. 

9.  f  of  16;  of  20;  of  30;  of  40. 

10.  At  30  ct.  a  dozen  for  oranges,  and  24  ct.  a 
dozen  for  lemons,  what  will  J  doz.  of  each  cost? 


FRACTIONS  193 

ORAL   EXERCISE 

1.  Draw  this  rectangle  on  the  blackboard,  and 
point  to  J  of  it ;  to  -J- ;  to  -| . 

2.  From  the  picture  show  that 

g"  —  ¥  =  2"* 

3.  If  you  call  the  rectangle  2, 

point  to  1;  to  £;   to  I£ ;  to  1J  — -J-.     How  much 

Jsli-t? 

4.  In  the  same  way,  point  to  1J— f .     How  much 

^is  it? 

5.  How  much  is  If  —  J? 

6.  Calling  the  whole  rectangle  1,  point  to  |  —  i; 

to  |  —  J;  to  f  —  J;  to  f  —  |. 

If  we  ask  for  the  sum  of  3  apples  and  1  orange,  the 
answer  cannot  be  apples  alone,  nor  oranges  alone.  But 
if  we  ask  for  the  sum  of  3  pieces  of  fruit  and  1  piece 
of  fruit,  the  answer  is  4  pieces  of  fruit.  In  adding,  we 
think  of  things  as  having  the  same  name. 

In  the  same  way,  if  we  ask  for  the  sum  of  |  and  J, 
the  answer  cannot  be  fourths  alone,  nor  halves  alone. 
But  if  we  ask  for  the  sum  of  |  and  J,  the  answer  is  ^, 
or  1^.  In  adding,  we  think  of  fractions  as  having  the 
same  name. 

That  which  tells  the  name  of  the  parts  is  the  number 
below  the  line.  It  is  called  the  denominator. 

That  which  tells  the  number  of  the  parts  is  the 
number  above  the  line.  It  is  called  the  numerator. 

To  add  or  subtract  fractions,  they  are  thought  of  as 
having  the  same  denominator. 


194-  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  How  much  is  f  +  1?  f  +  f?     f  +  £? 

2.  How  much  is  f-i?  f-f?     f-i? 

3.  How  much  is  |  +  1?  H  +  f?     2£  +  f? 

4.  How  much  is  f  -|?  1|-|?     2{-£? 

5.  How  much  is  f+i?  |-|?    H  +  |?    1|-|? 

The  teacher  should  resort  to  diagrams  on  the  blackboard  or 
to  the  use  of  objects  whenever  necessary,  but  not  otherwise. 

6.  How    much   is   -V-  +  t?      *£-§?      H  +  t? 

H-f? 

7.  How  much  is  2f  +  |?     2f  +  |?     2|  +  |,  or 


8.  How    much    is    3f  +  f?     3f-f?     5f  +  lf? 

|  +  i?     6|  +  f,or6 

9.  How  much  is 
^-^?     3^-2^? 
10.  How  much  is 


To  add  25  1  and  32^,  you  may  think  of      jjljf 
\  as  |,  and  add  thus  :  57-y-  =  58| 

To  subtract  25J  from  32J-,  you  may  also       324  =  3P-2- 
think  of  the  ^  as  |,  and  subtract  thus  :  25I 

6I 


WRITTEN  EXERCISE 


2.  29t-17f.  3.  43i  -Bl\ 

4.  33f  +  21f.        5.  33|-21f.  6. 

7OK  1  _L  1  Q  7                Q  OK  1         T  Q  7  o 

.  £o-£  i  ±0^-.         o.  ^04-     lo-A-.  y. 

10.  32^  +  14f.       11.  32£-14f.  12.  39|-20f. 


FRACTIONS  19S 

ORAL  EXERCISE 

1.  If  you  divide  a  line  into  3  equal  parts,  what 
is  the  name  of  each  part  ?     If  you  take  2  of  the 
parts,  you  have  what  fraction  of  the  line? 

2.  In  the  fraction  which  you  found,  what  is  the 
name  of  the  parts  ?     Then  what  is  the  denomi- 
nator ?     What  is  the  number  of  the  parts  ?     Then 
what  is  the  numerator  ? 

3.  If   you   divide   a   circle  into   5  equal  parts, 
and  color  2  of  them  red  and  1  blue,  what  part  is 
red  ?   What  part  is  blue  ?   What  part  is  uncolored  ? 
Name  the  numerators  and  the  denominators. 

4.  If  you  divide  a  line  into  10  equal  parts,  and 
color  3  of  the  parts  red  and  the  rest  blue,  the  red 
is  what  part  of  the  line  ?     The  blue  is  what  part  ? 
Name  the  numerators  and  the  denominators. 

WRITTEN  EXERCISE 

1.  Draw  a  rectangle  4  in.  long  and  1  in.  high. 
Divide  it  into  8  equal  rectangles,  each  ^  in.  long. 
Shade  f  of  the  rectangle. 

2.  Copy,  writing  in  the  missing  numbers  : 

t+i=i=T  1+1=1=1 

1+1=1+1=1       f+i=f+i=i 

3.  Copy,  writing  in  the  missing  numbers : 


196  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  If  we  divide  an  apple  into  thirds,  and  each 
third  into  halves,  what  parts  have  we  ? 

2.  From  this  cutting  of  the  apple  we  see  that 
i  of  |  is  what  fraction?     How  much  is  ^  of  J? 

'  3.  How  much  is  £  of  12?   £  of  12?   £  of  £  of  12? 
'  £  of  £  of  12  ?   i  of  12  ?   f  of  12  ?   i  of  f  of  12  ? 

4.  Draw  on  the  blackboard  a  line  6  in.  long,  and 
mark  off  the  inches.     Point  to  ^  of  the  line  ;  to  |; 
to  £;    to  -J-of  i;  to  I;  to  £  of  f 

5.  How  many  inches  are  there  in  ^  ft.?  in  J  ft.? 
inj  of  |  ft.?    in  £  of  Jft.? 

6.  Draw  this   figure   on 
the  blackboard.    Show  from 
it   that   i  of    f  =  i;  that 
=  l;  and  that  1-|  =  |. 

WRITTEN  EXERCISE 

1.  Draw  a  line  and  divide  it  so  as  to  show  that 

oH=|. 

2.  Draw  a  line  and  divide  it  so  as  to  show  that 

<**«*• 

the  following  and  write  the  results: 


3. 

i  of  18, 

i  of  18, 

i  of  18, 

|  of  18. 

4.  , 

I  of  24, 

1  of  24, 

i  of  24, 

|  of  24. 

5. 

\  of  30, 

f  of  30, 

i  of  30, 

f  of  30. 

6. 

}  of  36, 

|  of  36, 

i  of  36, 

|  of  36. 

7. 

I  of  42, 

i  of  42, 

i  of  42, 

j  of  42. 

MIXED   NUMBERS  197 

ORAL  EXERCISE 

1.  Add  10£,  9£,  2f 

2.  Add  15$,  41,  31. 

3.  Add  121,  2{,  i,  5. 

4.  From  10|  subtract  5|. 

5.  From  20|  subtract  5 ;  then  subtract  |. 

6.  From  15|  subtract  5f  ;  then  subtract  f. 

7.  If  your  books  weigh  2J  lb.,  and  you  weigh 
57f  lb.,  how  much  do  you  and  the  books  weigh? 

8.  If  you  need  7f  yd.  of   carpet  for  a   school 
platform,  and  3f  yd.  for  the  steps,  how  much  do 
you  need  for  both  ? 

WRITTEN  EXERCISE 

Add  the  numbers  in  Exs.  1-8 : 

1.  223!    2.  4211    3.  226£    4.  1129f 


42$     2371     342i     6342| 


'f 
65|     342|     427^     4826J 


5.  142$  6.  329|  7-  419|  8- 

273^  247|  1271  4623J 

821|  833f  2931  6481f 

227|-  607^  427|  892^ 

Subtract  in  Exs.  9-16  : 

9.  8426^  10.  21631  11.  8240f  12.  4035± 

40251  293^  642-i  63Q| 


13.  81421  14.  40211  15.  2003£  16.  4223J 
296!      683f      729|      826f 


198  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  How  much  is  £  of  42?   f  of  42? 

2.  How  much  is  |  of  88?   f  of  88?  f  of  88? 
1  of  88? 

3.  How  much  is  £  of  36?   f  of  36?   \  of  $48? 

f  of  $48? 

4.  How  much  is  |  of  $5.05?  f  of  $5.05?  f  of 

$5.05?  |  of  $5.05? 

We  call  the  taking  of  J  of  12  the  multiplication  of 
12  by  |.  When  we  use  the  sign  x  in  multiplying  by 
a  fraction,  we  read  it  "  of."  Thus,  f  X  15  is  read 
"f  of  15." 

To  multiply  15  by  f ,  you  have  seen  that  you  take 
|-  of  15,  which  is  5,  and  multiply  this  by  2,  giving  10. 

WRITTEN  EXERCISE 

1.  |  of  63.  2.  f  of  75.  3.  f  of  96. 

4.  f  of  68.  5.  |  of  72.  6.  f  of  96. 

7.  I  of  75.  8.  |  of  75.          9.  |  of  75. 

10.  |  of  66.  11.  f  of  72.         12.  f  of  96. 

13.  f  of  168.          14.  I  of  184.       15.  f  of  232. 
16.  I  of  344.          17.  f  of  424.       18.  f  of  568. 

19.  Rob   has    56    chickens    and   f   of   them    are 
white.     How  many  are  white? 

20.  Will  has  12  doz.  marbles  and  |  of  them  are 
glass.     How  many  marbles  are  glass? 

21.  There  are  336  pupils  in  a  certain  school  and 
f  are  boys.     How  many  are  boys  ? 


MIXED   NUMBERS 


199 


by  3f. 


ORAL  EXERCISE 

1.  How  much  is  f  of  40?    If  times  40? 

2.  How  much  is  f  of  10?  If  times  10? 

3.  Multiply  20  by  3;  by  |;  by 

4.  Multiply  16  by  2;  by  £;  by  2$;  by  2f;  by  2f. 

5.  How  much  is  2  J  times  20?  40?  50?  100?  200? 

6.  How  much  is  2*  times  6?  9?  12?  15?  18?  21? 

You  have  seen  that  to  multiply 
a  number  by  23  you  first  multiply 
by  3  and  then  by  20,  and  add 
the  results.  So,  to  multiply  by 
2|,  you  first  multiply  by  f  and 
then  by  2,  and  add  the  results. 


165 

2f 
99  product  by    | 

330        "    .     "  _2_ 
429        "         "  2| 


Multiply : 

1.  141  by  2f 

4.  145  by  6f . 

7.  $125  by  2f 

10.  $6.40  by 2|. 


WRITTEN  EXERCISE 


2.  156  by  3|.  3.  184  by  5|. 

5.  606  by  11J.  6.  426  by  llf. 

8.  $225  by  4|.  9.  $175  by  3|. 

11.  $8.20  by  5f.  12.  $4.08bylO|. 


14.  $26.52 


13.  $27.50 

12i    

17.  $31.15  18.  $42.75 


33^ 


15.  $15.51  16.  $14.55 
66f      161 


32| 


19.  $60.05    20.  $41.35 
14| 


21.  What  will  6f  yd. of  cloth  cost  at  $2.40  a  yard? 

22.  What  will  7|  yd.  of  silk  cost  at  $3.20  a  yard? 

23.  What    will    3|   doz.   fountain   pens    cost    at 

$1.20  each? 


200  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  Tell  the  cost  of  some  kind  of  cloth.     How 
much  will  10  J  yd.  cost? 

2.  Tell  the  cost  of  a  pair  of  shoes.     How  much 
will  2  pairs  cost  ? 

3.  If  a  man  earns  $3  for  10  hours'  work,  how 
many   hours   must  he    work    to    earn  enough  to 
buy  his  daughter  a  pair  of  shoes  at  $1.50? 

4.  How  many  hours  must  he  work  to  earn  enough 
to  buy  a  $6  suit  of  clothes  for  his  son? 

WRITTEN  EXERCISE 

1.  Sarah's  mother  bought  4£  yd.  of  cloth  for  a 
cloak,  at  $1.25  a  yard.     What  did  she  pay  for  it? 

2.  She  also  bought  3|-  yd.  of  lining  at  50  ct.  a 
yard,  and  4^  yd.  of  braid  at  20  ct.  a  yard.     How 
much  did  these  cost? 

3.  She  also  bought  6  pearl  buttons  at  $1.50  a 
dozen,  and  2  spools  of  silk  at  8  ct.  a  spool.     How 
much  did  these  cost? 

4.  The  dressmaker  charged  $5  for  making  the 
cloak.     What  did  materials  and  making  cost? 

5.  John's  mother  bought  2J  yd.  of   goods  for 
a  coat,  at  $1.20  a  yard,  and  2|  yd.  of  lining  at 
48  ct.  a  yard.     How  much  did  these  cost? 

6.  She  also  bought  a  dozen  buttons  at  25  ct.  a 
dozen,  and  2  spools  of  silk  at  8  ct.  a  spool,  and 
paid  $3  for  making.    How  much  did  the  coat  cost? 


REVIEW  201 

WRITTEN  EXERCISE 

Multiply  in  Exs.  1-24: 

1.  321  x  123.  2.  286  x  268. 

3.  242  x  375.  4.  481  x  192. 

5.  327  x  228.  6.  183  x  427. 

7.  231  x  247.  8.  820  x  102. 

9.  207  x  306.  10.  401  x  209. 

11.  608  x  103.  12.  201  x  208. 

13.  160  x  340.  14.  218  x  316. 

15.  708  x  130,  16.  300  x  140. 

17.  $27.42  by  69.  18.  $29.36  by  78. 

19.  $68.39  by  75.  20.  $41.78  by  69. 

21.  $181.75  by  65.  22.  $235.40  by  96. 

23.  $371.82  by  64.  24.  $491.30  by  82. 

Divide  in  Exs.  25-41: 

25.  4860  by  30.  26.  2940  by  70.  27.  3840  by  80. 
28.  2639  by  30.  29.  4862  by  70.  30.  2983  by  80. 
31.  6437  by  50.  32.  4963  by  60.  33.  8274  by  40. 
34.  83,468  •*•  308.      35.  48,884  +  202. 
36.  55,825  +  275.      37.  38,720  -*•  128. 
38.  81,375  -  250.      39.  56,520  *  240. 
40.  16,421  •+• 153.      41.  22,742  +  204. 

Multiply  in  Exs.  42-51  : 

42.  236  by  15f.  43.  327  by  16f.  44.  296  by  16f 
45.  345  by  23f  46.  288  by  17f.  47.  824  by  25f. 
48.  291  by  127$.  49.  345  by  125f .  50.  488byl37|. 
51.  2746|  + 14|  +  196f  +  328|  + 146^  +  261f .. 


202  PRIMARY   ARITHMETIC 

WRITTEN  EXERCISE 

In  Exs.  1-12,  first  perform  the  operation  indi- 
cated in  the  parenthesis : 

1.  6278  -  (142  +  387). 

2.  4821  -(2873-684). 

3.  |  of  (14f  +  21  -  2£). 

4.  f  of  (21f  +  4£  -  If). 

5.  2834J  -  (186  J  +  249|). 

6.  4423i-(287i-142f). 

7.  2893|-(447i-329|). 

8.  6882f  -  (278|  -  149f). 

9.  22f  x  (16$  +  14J  +  3f). 

10.  21|  x  (216$  +  33|  +  6|). 

11.  27f  x(162f +  481-51). 

12.  12f  x  (243J  +  268f  +  4$). 

Divide : 

13.  91,280  +  65.  14.  87,892-43. 

15.  36,800-68.  16.  49,894-202. 

17.  41,250-275.  18.  58,100-175. 

19.  58,432-332.  20.  58,125-465. 

21.  85,794-384.  22.  81,468-374. 

23.  70,882-197.  24.  17,856-144. 

25.  30,576  -  126.  26.  20,366  -  105. 

27.  20,394  -  120.  28.  63,844  -  135. 

29.  32,426  -  225.  30.  77,316  -  378. 

31.  65,664-912.  32.  18,149-127. 

33.  39,895  -  (52|  +  89  +  27f  -  68|). 

34.  43,452  -  (231|  +  71 1  +  262|  -  139|). 


REDUCTION   OF   DENOMINATE   NUMBERS     203 
DENOMINATE   NUMBERS 

ORAL  EXERCISE 

1.  How  many  inches  are  there  in  2  ft.  4  in.? 

2.  How  many  inches  are  there  in  1  yd.  10  in.? 

3.  How  many  ounces  are  there  in  1  Ib.  10  oz.? 

4.  Express  8  oz.  as  a  fraction  of  a  pound.     Ex- 
press 1J  Ib.  as  ounces;  also  1J  Ib.  as  ounces. 

5.  Express  18  sq.  ft.  as  square  yards.     Express 
li  sq.  yd.  as  square  feet. 

Numbers  having  the  unit  of  measure  attached  are 
called  denominate  numbers. 

Thus,  2  ft.,  3  mi.,  $5,  are  denominate  numbers. 

In  the  above  examples  you  found  that  a  number  may 
be  expressed  with  different  denominations.  Thus,  11  Ib. 
may  be  expressed  as  24  oz.,  or  14  in.  as  11  ft. 

Express  64  in.  as  feet. 

Since  there  are  12  in.  in  1  ft.,  there  are  as  many  feet  in  64  in. 
as  there  are  12  in.  in  64  in. 

But  64  in.  ~-  12  in.  =  5,  and  4  in.  remainder. 

Therefore,  there  are  5  ft.  4  in.  in  64  in. 

Express  7  ft.  as  inches. 

Since  in  1  ft.  there  are  12  in.,  in  7  ft.  there  are  7  times  12  in., 
or  84  in. 

WRITTEN  EXERCISE 

Express : 

1.  21  qt.  as  pints.  2.  32  qt.  as  gallons. 

3.  22  bu.  as  pecks.  4.  12  da.  as  hours. 

5.   $23|-  as  cents.  6.  25  min.  as  seconds. 

7.  If  Ib.  as  ounces.  8.  540  sec.  as  minutes, 


204  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  Look  at  the    foot  rule   and  tell  how  many 
inches  make  a  foot. 

2.  Measure  the  yardstick  with  the  foot  rule  and 
tell  how  many  feet  make  a  yard. 

3.  Measure  16  J  ft.  along  the  floor.    Do  you  know 
what  this  length  is  called? 

4.  Do  you  know  of  two  houses  or  streets  near 
your  school  that  are  a  mile  apart  ? 

5.  How  many  feet  in  25  yd.?   in  33^  yd.? 

6.  How  many  yards  in  25  ft.?   in  45  ft.? 

The  teacher  should  assist  the  pupils  to  visualize  these  basal 
units.  In  cities  the  number  of  blocks  to  the  mile,  the  number 
of  rods  in  the  width  of  the  streets,  and  the  average  size  of 
building  lots  should  be  known. 

TABLE  OF   LENGTH 

12  inches  (in.)  =  1  foot  (ft.)- 

3  feet  =  1  yard  (yd.). 

16 1  feet  =  1  rod  (rd.). 

528O  feet  =  32O  rods  =  1  mile  (mi.). 

WRITTEN  EXERCISE 

1.  How  many  feet  in  5|-  yd.?     How  many  rods? 

2.  How  many  feet  in  J  mi.?   in  ^  mi.?  in  |  mi.? 

3.  How  many  rods  in  J  mi.?   in  ^  mi.?  in  %  mi.? 

4.  How  many  inches  in  1  yd.  ?   in  1  rd.  ?  in  1  mi.  ? 

5.  How  many  miles  in  640  rd.?    in  5440  rd.? 

6.  How  many  yards  in  792  ft.?   in  1065  ft.? 


AREA    OF    TRIANGLES 


205 


ORAL  EXERCISE 

1.  How  do  the  areas  of  these  triangles  compare 
with  the  areas  of  the  rectangles? 

2.  If  the  rectangle  A  is  called  1,  what  is  triangle  A? 
If  the  rectangle   is 

8  sq.  in.,  what  is  the 
triangle  ? 

3.  If  the  rectangle 
E  is  called  10,  what 
is  triangle  B  ? 

4.  If  rectangle  C  is  4  in.  long  and  6  in.  high, 
what  is  its  area?    What  is  the  area  of  the  triangle  ? 

The  base  of  a  figure  is  the  line  on  which  it  stands. 

You  have  found  that  a  triangle  is  equal  to  half  the 
rectangle  of  the  same  base  and  height. 

If  the  base  of  a  triangle  is  6  in.  and  the  height  is  10  in., 
the  area  is  |  of  10  X  6  times  1  sq.  in.,  or  30  sq.  in. 


WRITTEN  EXERCISE 

Find  the  perimeter  and  area  in  Exs.  1-3: 

1.  Rectangle:  length  31  ft.,  height  18  ft. 

2.  Rectangle:  length  50  ft.,  height  37  ft. 

3.  Rectangle :  length  15  ft.,  height  4^  ft. 

Find  the  area  in  Exs.  4-6 : 

4.  Triangle:  base  40  in.,  height  27  in. 

5.  Triangle:  base  47  yd.,  height  18  yd0 

6.  Triangle:  base  31  ft.,  height  24  ft. 


206 


PRIMARY   ARITHMETIC 


ORAL  EXERCISE 

1.  What  name  do  you  give  an  angle  less  than 
a  right  angle  ?  one  greater  than  a  right  angle  ? 

2.  Draw  upon  the  blackboard  the  three  kinds  of 
angles  about  which  you  have  learned.     Name  each. 

3.  Draw  upon  the  blackboard  two  parallel  lines ; 
two  vertical  lines ;  two  horizontal  lines. 

A  four-sided  figure  whose  opposite  sides  are  parallel 
is  called  a  parallelogram. 

WRITTEN  EXERCISE 

1.  Here  is  a  picture  showing  that  a  triangle  is  half 

of  a  parallelogram  of  the  same 
base  and  height.  Draw  one  for 
a  right-angled  triangle  and  one 
for  an  acute-angled  triangle. 

2.  What  is  the  area  of  a  rectangle  7  J  in.  by  8  in.  ? 
also  of  a  triangle  whose  base  is  7|-  in.  and  height 
8  in.  ?     Draw  a  picture  of  each. 

3.  Suppose  you  should  cut  from  this  parallelo- 

gram the  triangle  T  and  put 
it  over  where  X  is ;  what  kind 
of  a  figure  would  you  have  ? 
Draw  the  two  figures. 

We  see  from  Ex.  3  that  the  area  of  a  parallelogram 
equals  that  of  a  rectangle  of  the  same  base  and  height. 

4.  What  is  the  area  of  a  parallelogram  whose 
base  is  8^  in.  and  whose  height  is  6  in.? 


DENOMINATE   NUMBERS 


207 


ORAL  EXERCISE 

1.  The  cube  A  is  how  many  times  B  ?  C  ?    Then 
a  cube  3  in.  on 

an  edge  is  how 
many  times  one 
that  is  1  in.  on 
an  edge  ? 

2.  How  many 

feet  in  1  yd.?   Then  how  many  cubic  feet  in  1  cu.  yd.  ? 

3.  How  would  you   find  the  number  of   cubic 
inches  in  1  cu.  ft.?     Multiply  on  the  blackboard 
and  find  this  number. 

You  have  found  that 

12  X  12  X  12  times  1  cu.  in.  =  1  cu.  ft, 

3x3x3  times  1  cu.  ft.  =  1  cu.  yd. ; 
or  that 

1728    cubic  inches  =  1  cubic  foot  (cu.  ft.). 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.). 


WRITTEN  EXERCISE 

1.  A  bin  is  2  ft.  by  3  ft.  by  5  ft.     It  holds  how 
much  more  than  1  cu.  yd.? 

2.  A  box  is  20  in.  by  8  in.  by  10  in.     It  holds 
how  much  less  than  1  cu.  ft.? 

3.  How  many  cubic  inches  in  a  prism  5  in.  by 
17  in.  by  13  in.? 

4.  How  many  cubic  yards  in  a  schoolroom  21  ft. 
by  18ft.  by  12ft.? 


208 


PRIMARY   ARITHMETIC 


ORAL  EXERCISE 


1.  This  boy  is  4  ft.  high.  Estimate  the  dimen- 
sions of  this  wood  pile.  Do  you  know  the  name 
of -this  amount  of  wood? 


2.  Sugar  is  sold  by  the  pound.  How  is  coal 
sold?  How  is  cloth  sold?  How  is  wood  sold? 
What  are  the  dimensions  of  this  amount  of  wood  ? 

A  pile  of  wood  8  ft.  by  4  ft.  by  4  ft.  is  called  a  cord. 
A  cord  contains  8x4x4  times  1  cu.  ft.,  or  128  cu.  ft 


KEVIEW   OF   THE   TABLES 

3.  Give  the  table  of  time. 

4.  Give  the  table  of  weight. 

5.  Give  the  table  of  dry  measure. 

6.  Give  the  table  of  square  measure. 

7.  Give  the  table  of  liquid  measure. 


DENOMINATE   NUMBERS 


209 


ORAL  EXERCISE 

1.  The  great  monument  to  Washington  is  555| 
ft.  high.     This  is  555  ft.  and  how  many  inches? 

2.  It  is  55  ft.  square  at  the 
base.    It  is  about  how  many 
times  as  high  as  it  is  square  ? 

3.  If  the  monument  were 
560  ft.  high,  it  would  be  how 
many  times  as  high  as  a  40-ft. 
school  building? 

4.  Calling   the   monument 
555  ft.    high,    this    is    how 
many  times  the  height  of  a 
spire  that  is  111  ft.  high? 

WRITTEN  EXERCISE 

1.  The   base  being    55  ft. 
square,  what  is  its  area? 

2.  How  many  yards  high 
is  the  monument? 

3.  If  the  sides  were  rectangles  540  ft.  long  and 
55  ft.  wide,  what  would  be  the  area  of  each? 

4.  Then  the  volume,  up  to  the  sloping  top,  would 
be  how  many  cubic  feet? 

5.  If  half  of  this  volume  is  stone,  allowing  for 
elevator  and  stairs,  how  many  cubic  feet  of  stone  ? 

6.  If  this  stone  weighs  170  Ib.  to  the  cubic  foot, 
how  many  pounds  of  stone  are  there  ? 


210  PRIMARY   ARITHMETIC 


ORAL  EXERCISE 


1.  How  many  feet  are  8  in.  and  4  in.? 

2.  How  many  feet  are  1  ft.  8  in.  and  1  ft.  4  in.? 

3.  How  many  hours  are  100  min.  and  20  min.? 

4.  Add  2  hr.  40  min.  and  3  hr.  20  min. 


Denominate    numbers    are    added    much   like   other 

numbers.     For   example,    to    add    10    ft. 

n    •  ^    a    ^  •  ^-    i          10  ft-  9  m- 

9  in.  and    o    it.    8    in.,    we   may   think  : 

9  in.    and    8    in.    are    17   in.,    which    is     -T^~T  —  T~-  — 
1  ft.   5  in.      Adding  the   1  ft.  to  6  ft.  + 

10  ft.,  we  have  17  ft.    Therefore,  the  sum  is  17  ft.  5  in. 


WRITTEN  EXERCISE 

Add  in  Exs.  1-9 : 

1.  17  ft.  10  in.  2.  16  yd.  25  in.  3.  35  gal.  2  qt. 
29   10     37    13     47 3_ 

4.  91  ft.  7  in.   5.  97  yd.  1  ft.   6.  75  bu.  2  pk. 
62   8      63    2      89    3 
74 3_    127    0      66    0 

7.  89  Ib.  14  oz.  8.  63  yd.  2  in.  9.  59  Ib.  9  oz. 
16    6     87    15     72   8 
83 5_   135    14     67 6_ 

Weights  are  usually  given  in  pounds  and  fractions,  as  50  J  Ib. 
or  58|  Ib.  Lengths  are,  if  short,  usually  given  in  feet  and  inches, 
or  in  yards  and  a  fraction,  or  in  miles  and  a  fraction.  Gallons 
and  quarts  or  bushels  and  pecks  are  seldom  used  together. 


DENOMINATE   NUMBERS 


211 


ORAL  EXERCISE 

1.  How  much  is  18  in.  -  9  in.  ?    1  ft.  6  in.  -  9  in.  ? 

2.  How  many  inches  are  2  ft.  6  in.  —  1  ft.  9  in.? 

3.  How  much  is  1  hr.  40  min.  —  50  min.? 

4.  How  much  is  1  Ib.  4  oz.  —  9  oz.? 


Denominate  numbers  are  subtracted  much  like  other 
numbers.     For  example,  to  subtract  10  ft. 
9  in.   from  17  ft.  5  in.,  we  may  think: 
5    in.   —  9  in.  is  impossible,  but  we  see 
that   1  ft.    5  in.  -  9    in.  =  8   in.       Then 


17  ft.  5  in. 
10   9 


6  ft.  8  in. 
16  ft.  -  10  ft.  =  6  ft,,  for  we  have  used  1  ft.  of  the  17  ft. 


WRITTEN  EXERCISE 

1.  19  ft.  3  in.  -  5  ft.  7  in. 

2.  16  yd.  7  in.  -  12  yd.  20  in. 

3.  287  ft.  8  in.  -  175  ft.  10  in. 

4.  154  gal.  2  qt.  -  48  gal.  3  qt. 

5.  17  mi.  100  ft.  -  10  mi.  1000  ft. 

In  walking  a  man  sometimes   carries   a   pedometer 
(pe-dom'e-ter),  which  shows  the  num- 
ber of  miles  he  has  walked. 

6.  If  a  man  starts  with  it  set  at 
f  mi.?  how  far  has  he  walked  now 
that  the  hand   points  to  If  mi.? 
when  it  points  to  6  mi.? 

7.  If  he  starts  with  it  at  2imi., 
and  walks  until  it  indicates  9|  mi.? 
how  far  has  he  walked? 


212  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  Measure  the  length  and  width  of  your  geog- 
raphy.    How  many  square  inches  on  each  page? 

2.  Measure  the  length  and  width  of  your  arith- 
metic.   How  many  square  inches  on  each  page? 

3.  How   many   more   square    inches  in  a   4-in. 
square  than  in  a  2-in.  square  ?     The  first  is  how 
many  times  as  large  as  the  second? 

4.  There  are  two  rectangles,  one  5  in.  by  6  in., 
the  other  3  in.  by  10  in.     Find  the  area  of  each. 

5.  What  is  the  area  of  a  rectangle  8  in.  by  4  in.? 
What  is  the  area  of  a  rectangle  half  as  long  and 
half  as  high  ? 


WRITTEN   EXERCISE 


1.  Find  the  number  of  square  inches  in  a  rect- 
angle that  is  25  in.  by  36  in. 

2.  Draw  the  rectangle  in  Ex.  1,  using  |  in.  to 
represent  1  in. 

This  is  called  drawing  to  a  scale  of  J. 

3.  Compare  the  area  of  a  6-in.  square  with  that  of 
a  rectangle  4  in.  by  9  in.    Draw  each  to  a  scale  of  -J. 

Find  the  number  of  square  inches  in  the  rectangles 
having  the  sides  as  given  in  Exs.  Jf-9 : 

4.  38  in.  by  72  in.      5.  86  in.  by  53  in. 
6.  32  mi.  by  48  mi.     7.  314  ft.  by  76  ft. 
8.  79  yd.  by  792  yd.    9.  48  yd.  by  129  yd. 


COUNTING  213 

II.    LARGER   NUMBERS.     INTEGERS,   COMMON 
FRACTIONS,    AND   DECIMALS   RELATED 

COUNTING 

ORAL   EXERCISE 

1.  Count  by  10's  from  10  to  100. 

2.  Count  by  100's  from  100  to  1000. 

3.  Count  by  1000's  from  1000  to  10,000. 

4.  Count  by  10,000's  from  10,000  to  100,000. 

5.  Count  by  100,000's  from  100,000  to  900,000. 
A  thousand  thousand  is   called  a   million.     It 

is  written  1,000,000. 

6.  Count   by    1,000,000's    from    1,000,000    to 
10,000,000. 

A  thousand  million  is  called  a  billion.  It  is 
written  1,000,000,000. 

In  writing  numbers  you  have  already  learned  that  they 
are  grouped  by  threes.  These  groups  are  called  periods. 

The  different  places,  like  units',  tens',  hundreds',  are 
called  orders. 

T>_    •     j      .       Billions'     Millions'     Thousands'       Units' 
period        period  period          period 

T3  'd  T3 

f-c  SH  *H 

00  ^Wl03  ^w*05  "^w.50 

%      -*->  r<       00      -^  Q       &*      4*  O  '    9       ™ 

Orders  :      SSSsSwISwII 

27,346,298,735 

This  is  read:  twenty-seven  billion,  three  hundred 
forty-six  million,  two  hundred  ninety-eight  thousand, 
seven  hundred  thirty-five. 


214  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

Read  the  numbers  in  Exs.  1-9 : 

1.  123,476.         2.  468,305.          3.  600,006. 

4.  3,243,698.      5.  4,027,635.       6.  2,963,481. 

7.  27,403,207.     8.  41,263,305.     9.  40,278,000. 

10.  About  how  many  pupils  are  there  in  your 
school?  About  how  many  people  in  the  village  or 
city  where  you  live  ?  About  how  many  are  there 
in  the  state  in  which  you  live  ?  About  how  many 
people  in  the  United  States? 

WRITTEN  EXERCISE 

Write  in  ivords  the  numbers  in  Exs.  1-9: 
1.  427,355.        2.  268,268.         3.  100,001. 
4.  1,275,275.      5.  3,410,014.      6.  2,002,002. 
7.  2,473,621.      8.  32,217,217.    9.  123,624,735. 

10.  Write  the  number  having  6  in  the  units'  order 
of  millions'  period,  zeros  in  the  thousands'  period, 
and  275  in  the  units'  period. 

11.  Write  the  numbers :  twenty  thousand  twenty; 
two  million,  two  hundred  two ;  three  hundred  thou- 
sand, three  hundred  thirty-three. 

12.  Allowing   1  ft.  to    each   person,  how   many 
persons  would  it  take  to  make  a  line  1  mi.  long  ? 
10  mi.  long?  100  mi.  long?   200  mi.  long? 

13.  How  many  seconds  in  1  min.?   in  60  min., 
or  1  hr.?  in  24  hr.,  or  1  da.?  in  365  da.,  or  1  yr.? 
inlOyr.? 


ADDITION  215 

ADDITION 

ORAL  EXERCISE 

1.  18  oz.  =  1  lb.  +  how  many  ounces  ? 

2.  34  oz.  =  2  lb.  +  how  many  ounces  ? 

3.  Express  as  pounds  and  ounces  :  10  oz.  +  8  oz. ; 
15  oz.  +  15  oz.  +  4  oz. 

4.  Express  as  feet  and  inches :    17  in. ;    10  in. 
+  7  in.;  1  ft.  10  in.  +  7  in. 

You  have  already  seen  that  denominate  numbers  are 
added  much  like  other  numbers.  A  1K  Q 

TC  ID.     »/   OZ. 

In  this  example  you  should  o         7 

read   the    9  oz.  +  7  oz.  as  1  lb. ;  611 

do   not   stop   to   say    U16   oz."  -.011    ^ 

Read  the  ounces'  column  as  1  lb. 

11  oz.,  and  the  pounds'  column  (with  the  1  lb.  added) 

as  13  lb. 

WRITTEN  EXERCISE 

See  how  long  it  takes  to  add  these  correctly.  You 
will  save  time  by  adding  rapidly  from  the  bottom  up, 
checking  the  work  at  once  by  adding  from  the  top  down. 

3.  52  ft.  2  in. 

27  4 

14  1 

293  6 

72  8 

36  5 

90  2 


152.20 
27.40 

2.  52 

27 

lb.  2  oz. 

4 

14.10 

14 

1 

216.20 

317 

2 

34.30 

46 

5 

62.10 

74 

2 

47.10 

26 

3 

216  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

A  certain  family  of  six  persons  used  in  one  day : 
Bread     1  Ib.    8  oz.  Potatoes     2  Ib. 

Butter  5  oz.  Suet  8  oz. 

Milk       2  Ib.    8  oz.  Flour          1  Ib.  4  oz. 

Sugar  12  oz.  Molasses  6  oz. 

Meat      2  Ib.  Salt,  etc.  5  oz. 

1.  What  did  the  bread  and  butter  weigh? 

2.  What  did  the  bread  and  milk  weigh  ? 

3.  A  pint  of  milk  weighs  1  Ib.    How  many  pints 
were  used? 

4.  The  suet  weighed  what  part  of  a  pound? 

5.  On  an  average,  each  person  ate  what  part  of 
1  Ib.  of  meat  ?   what  part  of  1  Ib.  of  potatoes  ? 

WRITTEN   EXERCISE 

1.  What  is  the  total  weight  of  the  food  men- 
tioned above  ? 

2.  At  4  ct.  a  pound,  how  much  did  the  bread 
cost? 

3.  Express  the  weight  of  the  sugar  as  a  fraction 
of  a  pound.    At  8  ct.  a  pound,  how  much  did  it  cost? 

4.  If  1  pt.  of  milk  weighs  1  lb.?  how  many  quarts 
were  used  ?     If  this  cost  8  ct.  a  quart,  how  much 
did  it  all  cost? 

5.  The  meat  cost  18  ct.  a  pound,  and  the  pota- 
toes 2  ct.  a  pound.     How  much  did  both  cost  for 
this  family  ? 


SUBTRACTION  217 

SUBTRACTION 

ORAL  EXERCISE 


Subtract  : 

1. 

4. 
7. 
10. 

22  oz. 
14 

2. 
5. 
8. 
11. 

lib.    6oz. 
14 

3. 
6. 
9. 
12. 

$1.16 
.14 

18  in. 
10 

1  ft.    6  in. 
10 

|1.06 
.10 

368' 
•58. 

$3.42 
.21 

$4.80 
3.00 

|5.35 
.20 

6bu.  2pk. 
4        1 

2t  gal. 
H 

You  have  already  found  that  to  subtract    3  Ib.   6  oz. 
a  number  like  14  oz.  from  3  Ib.  6  oz.,  you  14 

may  think  of  2  Ib.  22  oz.  - 14  oz.  -  2  Ib.  8  oz.     2  Ib.   8  oz. 

WRITTEN  EXERCISE 

1.  6ft.  7  in. -2  ft.  8  in. 

2.  7  Ib.  4  oz:  -  5  Ib,  6  oz. 

3.  10  gal.  2  qt.  -  6  gal.  3  qt. 

4.  12bu.2pk.-8bu.3pk.". 

5.  $581.36 -$293.48.       6,  $723.94  -  $109.09, 

7.  Suppose  you  weigh  51  Ib.  9  oz.,  and  Frank 
weighs  56  Ib.  3  oz.,  and  the  cat  weighs  5  Ib.  10  oz.; 
how  much  do  the  three  weigh? 

8.  Subtract  the  weight  of  the  cat,  and  find  how 
much,  you  and  Frank  weigh.     Prove  your  answer 
by  adding  your  weight  and  Frank's. 


218  PRIMARY   ARITHMETIC 

MULTIPLICATION 

ORAL  EXERCISE 

Write  the  numbers  from  1  to  12  in  miscellaneous  order  upon 
the  blackboard.  Change  the  order  during  the  oral  work.  For 
example:  2,  7,  3,  10,  6,  9,  12,  4,  11,  8,  5. 

1.  Read  the  products  by  2,  3,  4,  and  so  on  to  12, 
from  left  to  right;  from  right  to  left. 

2.  Read  the  products  by  2,  with  4  added,  thus : 
8,  18,  10,  and  so  on.     In  the  same  way,  read  the 
products  by  3,  4,  and  so  on  to  12,  with  such  num- 
bers added  as  the  teacher  directs. 

3.  Read  the  product  of  each  number  multiplied 
by  itself. 

The  class  should  frequently  review  the  counting  exercises  and 
the  tables  of  multiplication.  Ex.  2  may  be  varied  indefinitely. 

WRITTEN  EXERCISE 

Multiply  as  indicated  in  Exs.  1-4 : 

1.  $2436  by  35.  2.  $4876  by  49. 

3.  $5927  by  76.  4.  $8702  by  125. 

5.  How  much  is  the  rent  of  a  village  house  per 
year,  at  $27  per  month? 

6.  How  much  is  the  rent  of  a  city  house  per 
year,  at  $83.33  per  month? 

7.  How  much  more  per  month  is  the  rent  of 
the  city  house  than  the  village  house?   also  per 
year  ?     Explain  orally  the  reason  for  this  differ- 
ence in  rent. 


MULTIPLICATION  219 

WRITTEN  EXERCISE 

Multiply  as  indicated  in  Exs.  1—8: 
1.  $2942  by  245.  2.  $3004  by  406. 

3.  $27.50  by  325.  4.  $39.75  by  223. 

5.  $29.32  by  440.  6.  $126.40  by  175. 

7.  $205.65  by  305.  8.  $462.78  by  264. 

9.  How  much  does  an  80-acre  field  in  the 
country  cost,  at  $65  an  acre? 

10.  How  much    does  a  20-acre  lot  adjoining   a 
village  cost,  at  $260  an  acre? 

11.  How  much  does  a  city  building  lot  40  ft.  on 
the  front  cost,  at  $130  per  front  foot? 

12.  It  is  desired  to  purchase  a  strip  of  land  1  ft. 
wide  and  40  ft.  deep,  so  as  to  widen  a  lot  for  an 
office  building  in  a  city.     How  much  will  it  cost, 
at  $130  a  square  foot? 

13.  A  man  has  a  farm  of  160  acres.     It  cost  him 
$75.25  an  acre.     What  was  the  total  cost? 

14.  A  man  has  a  city  lot  of  125  front  feet,  cost- 
ing him  $133.33  per  front  foot.     How  much  did 
the  lot  cost? 

15.  A  man  bought  a  piece  of  land  to  add  to  his 
lot  for  a  large  city  block.     The  piece  was  18  ft. 
wide  and  52  ft.  deep,  and  he  paid  $366.67  a  square 
foot  for  it.     How  much  did  it  cost  ? 

The  pupil  should  be  asked  to  compare  the  sizes  of  these  lots, 
and  also  to  compare  the  answers.  Without  computing  the  exact 
differences,  he  should  be  asked  to  explain  the  reason  for  the  great 
variations  in  value.  The  lots  in  Exs.  11  and  14  are  100  ft.  deep. 


220  PRIMARY    ARITHMETIC 

-  ORAL  EXERCISE 

1.  How  much  is  100  times  $0.15? 

2.  How  much  is  100  times  $1.25? 

3.  What  is  the  short  way  of  multiplying  a  num- 
ber expressing  United  States  money  by  10?  by  100  ? 

To  multiply  by  10,  move  the  decimal  point  one  place  to 
the  right ;  to  multiply  by  100,  move  it  two  places. 

Hence   to  multiply,   for   example,   $325.50  by  600, 
we  may  first  multiply  by  100,  writing  •    ~  ._ 

$32,550  as  the  new  multiplicand,  and 
then  we  may  multiply  this  by  6.  |195  3QQ 

If  there  are  zeros  in  the  multiplier,  it 
is  not  necessary  to  write  the  products  by  zero.     Thus, 

Instead  of  writing  all  this:  Write  only  this:- 

426  426 

305  305 

2130  product  by      5  2130 

0000        ".       «        0  tens  1278 

127800        "        "    300  129930 
129930        "        "    305 

WRITTEN   EXERCISE 

Multiply: 

1.  $6.25  by  400.  2.  $8.25  by  600. 

3.  $48.25  by  700.  4.  $62.50  by  500. 

5.  $36.75  by  800.  6.  $29.35  by  900. 

7.  $285.75  by  400.  8.  $823.30  by  600. 

9.  $981.03  by  200.  10.  $6327  by  505. 

11.  $2835 -by  805.  12.  $2083  by  609. 


REVIEW 


221 


ORAL  EXERCISE 

1.  Mollie  has  been  sent  to  buy  provisions  at  the 
bakers.   Shebought 

Jib,  of  cake  at  50 
ct.  a  pound,  and  a 
dozen  cream  puffs 
at  25  ct.  What  did 
these  co&t? 

2.  What   did  she 
pay  for  six  rolls  at 
10  ct.  a  dozen,  and 
a  pie  at  15  ct.? 

3.  She  bought  a 
10-ct.  loaf  of  brown 

bread,  and  three  8-ct.  loaves  of  whole  wheat  bread. 
What  did  these  cost? 

4.  She   handed   the   clerk    $1.25.     How   much 
change  did  she  get? 

WRITTEN   EXERCISE 

1.  If  the  baker  sells  36  doz.  cookies  at  10  ct.  a 
dozen,  and  they  cost  him  7|-  ct.  a  dozen,  how  much 
does  he  make  on  the  cookies  ? 

2.  If  it  costs  the  baker  3J  ct.  a  loaf  for  the  white 
bread,  6  ct.  a  loaf  for  the  brown  bread,  and  5j;Ct. 
a  loaf  for  the  whole  wheat  bread,  and  he  sells  in 
a  day  200  loaves  of  white  bread  at  5  ct.,  15;  of 
brown  at  10  ct.,  and  20  of  whole  wheat  at  8  ct»> 
how  much  does  he  make? 


222  PRIMARY   ARITHMETIC 

FRACTIONS 
ORAL  EXERCISE 

1.  The  fraction  |  of  a  dollar  means  that  $1  has 
been  divided  into  how  many  equal  parts,  and  how 
many  of  these  parts  taken? 

2.  In  the  fraction  •£-$,  what  is  the  denominator  ? 
What   does   it  tell  about  the  fraction?     What  is 
the  numerator?     What  does  that  tell? 

3.  The  fraction  $|  shows  that  how  many  quar- 
ter dollars  have  been  taken?     How  much  is  this? 
The  fraction  $|  shows  that  how  many  half  dollars 
have  been  taken?     How  much  is  this? 

A  fraction  less  than  1,  like  |,  is  called  a  proper  fraction. 

A  fraction  equal  to  or  greater  than  1,  like  ^  or  |-,  is 
called  an  improper  fraction. 

A  number  in  which  no  fraction  appears,  like  2,  10, 
56,  is  called  a  whole  number,  or  an  integer. 

A  number  made  up  of  an  integer  and  a  fraction,  like 
4|-,  is  called  a  mixed  number. 

WRITTEN   EXERCISE 

1.  Write  five   fractions,  five  integers,  and  five 
mixed  numbers. 

2.  Write    five    improper    fractions    equal  to  1, 
and  five  greater  than  1. 

3.  A  boy  earned  $1  in  one  day,  $f  the  next  day, 
and  $1|  during  the  next  two  days.     How  much 
did  he  earn  in  the  four  days  ? 


FRACTIONS  223 

REDUCTION   OF   FRACTIONS 

ORAL  EXERCISE 

1.  From  A:  J  =  J?   *  =  £?    J  =  l?   J  of  f  =  £=|? 

?  ?    l  _  ?_?     ?   _   1  ?    ?=~ 
Tor*    2"— 10-    10"  —  -1- •    5^     - 

4.  Express  J  as  fourths;  as  eighths;  as  sixths. 

5.  Express  J  as  sixths;  as  ninths;  f  as  sixths. 

Both  terms  of  a  fraction  may  be  multiplied  by  the  same 
number  without  changing  the  value  of  the  fraction. 

3  times  1       3 
=  6* 


Both  terms  of  a  fraction  may  be  divided  by  the  same 
number  without  changing  the  value  of  the  fraction. 


8         8  -2 


J.U        j. \j  ~=~~  ^        *j 

When  the  terms  of  a  fraction  are  divided  by  the  same 
number,  that  number  is  said  to  be  canceled. 

When  both  terms  cannot  be  divided  by  the  same  inte- 
ger, the  fraction  is  said  to  be  reduced  to  its  lowest  terms. 

Thus,  -g8g  =  ^V  =  y\  =  y>  its  lowest  terms. 

WRITTEN   EXERCISE 

1.  Reduce  to  twelfths :  |-?  J,  |,  £,  f,  J,  f . 

2.  Reduce  to  sixteenths :  %,  %,  |?  f ,  |,  f ,  |. 

3.  Reduce  to  lowest  terms :  f^-,  T92-?  ^^-,  £#,  |f. 


224  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  How  many  half  spheres  in  1  sphere?    in  1J 
spheres  ?  in  2  spheres  ?  in  2J  spheres  ? 

2.  How  many  halves    in  1?    in    Ij?   in   2?   in 
5?   in  51?    in  10?   in  25?  in  50? 

3.  How  many  fourths  in  1?    in  1£?   in  1J?   in 
If?   in  5f?  in  10?   in  25?   in  50? 

4.  Express  as  thirds :  8,  2,  3  J,  4,  5f ,  7,  10f 

5.  Express  as  fourths :  6,  8,  2{,  5,  3|,  8J,  12. 

6.  Express  as  fifths:  9,  6,  4|,  3f,  8f,  7|,  11. 

7.  Express  as  sixths:  1,  6,  7i,  8f,  11,  IQi,  9. 

8.  Express  as  eighths:  10,  7,  6J,  7f,  9|,  10|. 

9.  Express  as  tenths :  1,  5,  2^,  7>  3T%,  11. 

Required  to  reduce  14^V  to  twelfths. 

12  ,         14  times  12      168 
Smcel^-,14,        — -        _. 

Adding,   W+  A=W- 


WRITTEN    EXERCISE 

Reduce : 

1.  69  to  eighbhs.  2.   77  to  ninths. 

3.   91  to  sevenths.  -4.  96  to  ninths. 

5.  98  i-  to  halves.  6.  341  to  tenths. 

7.  17|  to  fifths.  8.  73f  to  fifths. 

9.  83f  to  thirds.  10.  48f  to  thirds. 

11.  66|  to  sixths.  12.  39f  to  fourths. 

13.   98T9o  to  tenths.  14.   lOlf  to  fourths. 

15.  35f  to  sevenths.  16.  67^  to  twelfths. 


REDUCTION    OF    FRACTIONS  225 

ORAL  EXERCISE 

1.  How  many  whole  squares  can  you  make  from 
these  8    quarter  squares?    from    4    such    quarter 
squares  ? 

2.  Then  f   are  how  many  units?     ^  are   how 
many  units  ?   f  =  1  +  how  many 

fourths?  f  =  l  +  what  fraction? 

3.  How  many  2-ft.  lengths 
in  10  ft.  ?    Howr  many  times  is 

$2  contained  in  $10?     How  many  f  in  -1/?    How 
many  f  in  -L0-?     Then  how  many  IV  in  -12°-?   in  f  ? 

4.  How  many  2-ft.  lengths  in  5  ft.?    How  many 
|  in  |?   in  |?   How  many  1's  in  f  ?   in  -^? 

5.  Since  f  — 1,  how  many  1's  in  y?   in -^6-?   in 
-V8-?    in  |?    in  I?     How  many  1's  in  f  ?  in  J? 

Required  to  reduce  ^9-  to  a  whole  or  a  mixed  number. 
Since  %  =  1,  -3/  =  as  many  1's  as  39  +  7,  or  5f . 

To  reduce  a  fraction  to  a  whole  or  a  mixed  number, 
divide  the  numerator  by  the  denominator. 

WRITTEN  EXERCISE 

Reduce  to  whole  numbers : 
1.  _4_s_.  I  2.  ¥.     3.  .11.1.     4.  _y>.     -5.  Y-       6.  ^. 

Seduce  to  mixed  numbers  : 
7. \8_2_.     s.  -V3-.     9.  -\7-.     10.  ii^-.     11.  -V-.     12.  -2T°T6-. 

Reduce  to  whole  or  to  mixed  numbers :  . 
13.  Y--    14.  -y~.   15.  ff     16.  -yj-.     17.  -W7-.  18.  -y/. 


226  PRIMARY   ARITHMETIC 

ALIQUOT   PAETS 

WRITTEN   EXERCISE 

1.  Multiply  246  by  5.     Divide  2460  by  2.    Com- 
pare the  results. 

2.  Instead  of  multiplying  by  5,  you  may  annex 
how  many  ciphers  and  divide  by  what  number  ? 

3.  Multiply  224  by  25.      Divide  22,400  by  4. 
Compare  the  results. 

4.  Instead  of  multiplying  by  25,  you  may  annex 
how  many  ciphers  and  divide  by  what  number  ? 

Because  5  =  10  -*-  2,  therefore,  to  multiply  by  5,  annex 
a  cipher  and  divide  by  2. 

Because  25  =  100  -f-  4,  therefore,  to  multiply  by  25, 
annex  two  ciphers  and  divide  by  Jf. 

5.  Divide  240  by  5.     Multiply  24  by  2.     Com- 
pare the  results. 

6.  Instead  of  dividing  by  5,  you  may  cut  off 
how  many  ciphers  and  multiply  by  what  number  ? 

7.  Divide  300  by  25.     Multiply  3  by  4.     Com- 
pare the  results. 

8.  Instead   of    dividing    by   25,   you    may   cut 
off    how   many .  ciphers    and   multiply    by   what 
number  ? 

Therefore,  to  divide  tens  by  5,  cut  off  a  cipher  and 
multiply  by  2. 

To  divide  hundreds  by  25,  cut  off  two  ciphers  and 
multiply  by  £• 


ALIQUOT   PARTS  227 

ORAL  EXERCISE 

Multiply  as  indicated*in  Exs.  1-12 : 
1.  86  by  5.  2.  36  by  5.  3.  28  by  5. 

4.  44  by  25.         5.  84  by  25.         6.  64  by  5. 
7.  64  by  25.         8.  48  by  25.         9.  88  by  25. 

10.  248  by  5.       11.  202  by  5.       12.  124  by  5. 

Divide  as  indicated  in  Exs.  13-18 : 

13.  110-5.         14.  210-5.         15.  320-5. 

16.  600-25.       17.  800-25.       18.  500-25. 

An  integer  or  mixed  number  that  will  exactly  divide 
a  number  is  called  an  aliquot  part  of  that  number. 
For  example,  you  have  found  (page  157)  that 
10.50  is  1  of  $1,  $0.331  is  i.  of  $1, 

$0.25  is  1  of  $1,  $0.20  is  \  of  $1. 

Therefore,  $0.50,  $0.25,  $0.331,  $0.20  are  aliquot  parts 
of  $1.00,  and  5  is  an  aliquot  part  of  10.      $0.121  =  $1 . 

The  term  is  unimportant,  but  is  required  in  some  courses. 
WRITTEN  EXERCISE 

Multiply  as  indicated  in  Exs.  1-3: 
1.  3133  by  5.     2.  387  by  25.     3.  7354  by  25. 

Divide  as  indicated  in  Exs.  ^-6 : 
4.7070-5.      5.8400-25.    6.31,200-25. 

7.  At  5  ct.  each,  what  will  147  pencils  cost? 

8.  At  25  ct.  each,  what  will  147  books  cost? 

9.  If  5  ponies  cost  $430,  what  will  1  cost? 
10.  If  25  pianos  cost  $7100,  what  will  1  cost? 


228  PRIMARY   ARITHMETIC 

ADDITION   OF   FRACTIONS 

ORAL  EXERCISE 

1.  Add :  4|-  +  31,  6i  +  7f ,  5f  +  7f ,  41  +  5|. 

2.  Add :    J  +  J?  i  +  i?  i  +  |?  i  4-  iV  or  T2o  +  iV 

3.  Add  :    |  +  |,  |  +  i  i  +  f     To  add  i  and  i, 
should  we  think  of  both  as  fourths  or  as  eighths  ? 

You  have  found  that  to  add  fractions  they  should  be 
reduced  to  fractions  having  a  common  denominator. 

In  Ex.  3  you  found  that  it  is  bet-          _ 
terto  reduce  to  fractions  having  the        *  _     7^f 
least  common  denominator  (l.c.d.).  ^  |"|  _ 

Because  the  denominators  are  4 
and  6,  the  l.c.d.  must  contain 

4-2x2 

and  6-2x3, 

and  therefore  two  2's  and  a  3.     Therefore, 
the  l.c.d. -2  x  2  x  3  =  12. 

We  also  see  that  f  =  ^  f  =  \%.     (See  page  223.) 

WRITTEN   EXERCISE 

Ili2  92j_4  ^2il 

*•     3  +"5'  *•     *•*>*  5-+2~' 

'  4.  2|  +  4i  5.  31  +  51  6.  4f +  31. 

Do  4       '  o  o  D 

7O3     i    Al  Q      31     i    9  1  Q      *71   _i_  AT 

.    ^f  +  4fcf.  O.    0-g-  +  ^1TQ-.  ».     /^   -     Og-. 

10.  If  a  man  paid  $3f  for  a  hat  and  $161  for  a 
coat,  how  much  did  he  pay  for  both? 

11.  A  man  bought  3  cows  for  $100.    He  sold  one 
for  what  it  cost,  another  for  $351,  and  the  third 
for  $42|.     How  much  did  he  receive  for  all? 

TT  *± 


FRACTIONS  229 

SUBTRACTION  OF  FRACTIONS 

ORAL  EXERCISE 

1.  Subtract :  f  -  l,  f  -  l,  f  -  J,  f  -  f . 

2.  Subtract:  4f  -  21,  7|  -  41,  18f-8i,25|  -  5f. 

3.  From   $5f   subtract   $1;    then  subtract   $1; 
then  $21. 

4.  From  10  ft.  6  in.  subtract  6  ft.  4  in.     From 
lOf  subtract  6f 

5.  In  order  to  subtract  fractions,  what  should 
you  do  with  their  denominators? 

To  subtract  one  fraction  from  another,  they  should  be 

reduced  to  fractions  having  the  least  common  denominator. 

How  much  is  426f  -  1251  ?  ^  = 

The  l.c.d.  of  the  fractions  is  12,  for     -toe? 

this  is  the  smallest  number  that  con-  ¥  ~~ 

tains    3    and    4.     We  see  (page  223)  *¥ 

that  |  =  T8^-,  and  ^  =  ^.     We  then  subtract  as  shown 

on  page  180. 

WRITTEN  EXERCISE 

Subtract  in  Exs.  1-9: 

1.  481  -  30i.       2.  625|  -  72f      3.  833^  -  66f . 
4.  1121  -  89|.     5.  1051  -  92f.      6.  691  _  67f 
7.  245TV-45f.  8.  312f-121ii    9.48^-211. 

10.  A  man  bought  some  property  for  $92|?  and 
sold  it  for  $1051.     How  much  did  ha  gain? 

11.  How  much  would  he  have  gained  if  he  had 
-sold  it  for  $1061? 


230 


PRIMARY   ARITHMETIC 


ORAL  EXERCISE 


1.  If  Kate  used  ^  Ib.  of  sugar  at  6  ct.  a  pound, 
7  lemons  at  2  ct.  each,  and  a  4-ct.  orange  for  the 
lemonade  at  her  party,  what  did  it  cost? 


2.  At  40  ct.  a  quart,  how  much  did  3  pt.  of  ice 
cream  cost? 

3.  At  £  Ib.  to  the  cup,  what  did  2  cups  of  sugar 
for  the  cake  cost,  at  6  ct.  a  pound  ? 

4.  At  18  ct.  a  dozen,  what  did  4  eggs  for  the 
cake  cost? 

5.  For  icing  the  cake,  1  egg  and  1  cup  of  sugar 
were  used.     How  much  were  these  worth  at  the 
prices  given? 

6.  Write  all  these  items  on  the  board  and  tell 
what  Kate's  party  cost. 


FRACTIONS  231 

ORAL  EXERCISE 

1.  If  A  is  called  1,  point  to  |;  f ;  f ;  |. 

2.  Point  to  ^  of  |.     How  much  is  it? 
3.  Point  to  \  of  |.     How  much  is  it? 
4.  Point  to  |  of  |.     How  much 
is  it? 

5.  If  B  is  called  1,  point  to  \\ ; 

3.1.1 
¥?    ?>    ¥• 

6.  Point  to  I  of  If  How 
A     B     c     D     E         much  is  it  ? 

7.  Point  to  ^  of  J.     How  much  is  it  ? 

8.  Using  blocks  or  strips  of  paper  or  pictures, 
show  that  J  of  ^  is  ^,  and  ^  of  J  is  \. 

9.  Show  that  f  of  ^  is  |,  and  that  f  of  f  is  J. 

WRITTEN  EXERCISE 

1.  Draw  a   line   1  in.  long  and  divide   it   into 
eighths. 

2.  Looking  at  this  line,  find  J  of  f  and  write 
its  value. 

3.  Looking  at  it  again,  find  ^  of  |  and  write  its 
value. 

In  the  same  way,  write  the  values  of: 

4.  i  of  f  5.  1  of  f.  6.  i  of  f . 
7.  |  of  f .                 8.  f  of  1.                9.  i  of  |. 

10.  Show  that  ^  of  |  in.  =  J  of  J  in. 

11.  Show  that  ^  of  |  of  a  15-in.  line  is  the  same 
as     of     of  the  line. 


232  PRIMARY   ARITHMETIC 


ORAL    EXERCISE 

1.  Point  to  J  of  the  rectangle;  to  £;  to  {;  to  f . 

2.  How  many  fs  in  J?  in  f ? 
inl? 

3.  How  many  |'s  in  £?  in  £? 
in  4?  in  1? 


4 


4.  Show  that  ^  is  ^  of  J.     In  the  same  way, 
|  is  what  part  of  ^  ? 

5.  Show  that  f  is  6  times  |.     In  the  same  way, 
f  is  how  many  times  ^?  how  many  times  J? 

6.  At  6  for  a  dime,  what  will  1J  doz.  eggs  cost? 

7.  At  a  quarter  of  a  dollar  each,  how  many  balls 
can  I  buy  for  half  a  dollar  ? 

8.  If  we  can  buy  8  tablets  for  $1,  how  many 
can  we  buy  for  50  ct.?   for  25  ct.?   for  75  ct.? 

9.  When  eggs  are  a  quarter  of  a  dollar  a  dozen, 
how  many  dozen  can  be  bought  for  $1.50?   for 


WRITTEN    EXERCISE 

1.  Draw  a  rectangle  twice  as  long  as  the  one 
above,  but  with  the  same  width,  and  divide  it  into 
16  equal  squares. 

2.  Look  at  it,  and  write  the  answers  to  these 
questions  : 

1.  TV  is  what  part  of  |?   of  \  ?   of  J? 

2.  How  many  times   is   ^g-   contained  in  1? 

in  |?   inf? 

3.  How  many  times  TV  is  f?  f  ?  1?  J? 


FRACTIONS  233 

ORAL   EXERCISE 

1.  What  number  does  f  equal?   J^?   -V6-?   V? 

2.  At  $|-  a  yard,  what  is  the  cost  of  8  yd.  of 
cloth?   of  10yd.?   of  16  yd.?   of  24  yd.? 

3.  At  $£  a  yard,  what  is  the  cost  of  6  yd.  of 
cloth?   of  12  yd.?   of  15  yd.?   of  30  yd.? 

4.  How  much  will  24  yd.  of  cloth  cost  at  50  ct. 
a  yard?   at  33^  ct.  a  yard? 

You  have  seen  that  30  times  50  ct.  is  the  same  as  30 
times  $£,  or"$-32°-,  or  $15.  Also  that  30  times  33£  ct.  is 
the  same  as  30  times  $l,  or  $10. 

In  the  same  way, 

60  times  25  ct.  =  60  times  $i  =  $&£  =  $15. 


60  times  20  ct.  =  60  times  $1-  =  f  M-  =  $12. 

o  o 

5.  What  is  the  cost  of  35  doz.  eggs  at  20  ct.  a 
dozen? 

6.  What  is  the  cost  of  84  doz.  oranges  at  50  ct. 
a  dozen? 

7.  What  is  the  cost  of  88  brooms  at  25  ct.  each? 
at  50  ct.  each? 

8.  What  is  the  cost  of  15  doz.  pencils  at  3  doz. 
for  a  dollar? 

9.  How  much  would  your  school  have  to  paj7 
for  25  boxes  of  crayons  at  20  ct.  a  box? 

10.  How  much  would  it  have  to  pay  for  60  readers 
at  33J  ct.  each?   for  40  at  25  ct.  each? 

11.  How  much  would  it  have  to  pay  for  4  maps 
at  50  ct.  each?  at  $3  each?   at  $3.50  each? 


234  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  How  much  will  12  yards  of  silk  cost  at  $J  a 
yard?   at  $1  a  yard?   at  $1.50  a  yard? 

2.  How  much  will  15  yards  of  silk  cost  at  $  ^  a 
yard?   at  $1  a  yard?   at  $1.33|  a  yard? 

3.  How  much  will  15  doz.  small  dolls  cost  at  $| 
a  dozen?   at  $1  a  dozen?   at  $1.20  a  dozen? 

4.  How  much  will  16  things  cost  at  $|  each? 
at  $1  each?   at  $1.25  each? 

You  have  found  that  the  cost  of  things  at 

$1.50  each  is  the  cost  at  $1  +  half  as  much  more; 
$1.33  J  each  is  the  cost  at  $1  -f-  a  third  as  much  more  ; 
$1.25  each  is  the  cost  at  $1  H-  a  fourth  as  much  more; 
$1.20  each  is  the  cost  at  $1  -f-  a  fifth  as  much  more. 
For  example,  at  $1.25  a  dozen,  a  dealer  would  pay 
for  12  doz.  boxes  of  candy  $12  +  \  of  $12,  or  $15. 

WRITTEN  EXERCISE 

1.  How  much  will  136  hats  cost  at  $1.25  each? 

2.  How  much  will  148  croquet  sets  cost  at  $1.20 
a  set? 

3.  How  much  will  250  tennis  rackets  cost  at 
$1.50  each? 

4.  How  much  will   96  pairs   of   shoes  cost  at 


5.  If  certain  books  cost  a  dealer  at  the  rate  of 
$1.25  apiece,  how  much  must  he  pay  for  132  such 
books? 


FRACTIONS  235 

ORAL  EXERCISE 

Copy  these  numbers  on  the  blackboard  and  add: 

4567 

44        55        66        77 

444      555      666      777 

1111    !>555    6666    77-77 

Point  to  the  columns  representing  the  following 
numbers,  and  tell  the  sums  in  all  cases: 

1.  10,  i  of  10,  f  of  10. 

2.  15,  !-  of  15,  f  of  15. 

3.  14,  lof  14,  f  of  14,  |  of  14. 

4.  21,  i  of  21,  f  of  21,  |  of  21. 

5.  28,  I  of  28,  |  or  i  of  28,  f  of  28. 

6.  12,  f  of  12,  i  of  12,  i  of  12. 

7.  8,  i  of  8,  §  of  8,  I  of  8. 

8.  10,  11  times  10;  12,  11  times  12. 

9.  18,  11  times  18,  1  of  18,  f  of  18. 

WRITTEN  EXERCISE 

1.  At  12J  ct.  a  yard,  how  much  will  7  yd.  of 
cloth  cost? 

2.  If   the  cloth  costs  2J-  ct.  a  yard  more,  how 
much  will  the  7  yd.  cost? 

3.  If  the  cloth  can  be  bought  for  15  ct.  a  yard, 
and  it  is  found  that  we  need  only  6^  yd.,  how  much 
will  it  cost? 

4.  How  much  would  6|  yd.  cost  at  18  ct.  a  yard? 


236  PRIMARY   ARITHMETIC 


WRITTEN   EXERCISE 

1.  261  -  17f        2.  331  - 16|.       3.  21|  - 

4.  $4f  +  $5i.      5.  $6i  +  $7f      6. 

7.  26|  +  18i.       8.  42T52 -29f.     9. 
10.  28TV-19|.    11.  45T\-26£.    12.  45I27r_18i. 
13.  |in.  +  2|in.  14.  If  ft.  +  i  ft.  15.  2|in.  +  f  in. 

16.  A  man  bought  62|  Ib.  of  maple  sugar,  and 
sold  81  Ib.,  5|  Ib.,  6f  Ib.     How  much  had  he  left? 

17.  A  man  bought  4^  doz.  eggs,  6J  doz.,  5J  doz., 
and  3J  doz.      He  then  sold  12|  doz.  and  2  doz. 
How  many  had  he  left? 

18.  What  are  40  eggs  worth  at  15  ct.  a  dozen? 

19.  What  are  20  oranges  worth  at  45  ct.  a  dozen? 

20.  What  will  8  yd.  of  cloth  cost  at  $f  a  yard? 

21.  {  of  48,  f  of  48.  22.  i  of  60,  |  of  60. 
23.  i  of  42,  |  of  42.  24.  \  of  42,  f  of  42. 
25.  I  of  64,  f  of  64.  26.  i  of  27,  f  of  27. 
27.  f  of  36  in.;  of  48  in.  28.  f  of  $63 ;  of  $81. 
29.  f  of  72  yd. ;  of  96  rd.  30.  f  of  35  ft. ;  of  75  in. 

31.  If  I  need  56  ft.  of  picture  molding  for  one 
room  and  |  as  much  for  another,  how  much  do  I 
need  for  both  ? 

32.  If  John's  father  buys  3  qt.  of  one   kind  of 
lawn  grass  seed,  and  2J  times  as  much  of  another 
kind,  how  many  quarts  has  he  of  both? 

33.  If   one   room   takes    27  yd.   of   carpet,  and 
another  f  as  much,  and  a  third  J  as  much  as  the 
first  two  together,  how  much  is  required  for  all? 


BILLS   AND   RECEIPTS 


237 


BILLS   AND   RECEIPTS 

What  do  people  mean  when  they  say  they  have 
an  account  at  a  store  ?  What  is  meant  by  present- 
ing a  bill  for  goods  purchased  ?  What  is  meant  by 
receipting  a  bill?  How  is  it  done? 

In  the  bill  given  below  the  symbol  @  means  at.    For 
example,      2  doz.  eggs  @  SOX         $0.60 
means  that  2  doz.  eggs  at  30  ct.  a  dozen  cost  60  ct. 

To  fill  a  bill  means  to  write  the  cost  of  each  item. 

To  foot  a  bill  means  to  add  and  find  the  total  cost. 

Dr.  means  debtor,  and  in  the  bill  below  it  means  that 
David  Brownson  is  in  debt  to  Jewett  &  Glover. 


21,  1905. 


W&ot  88th, 


Ifovk. 


^7o  Jeivett  &-  S  lover, 
3)eaters  in  Groceries,  535  West  80th  St.,      3)r. 


,.  5.       6 


.  Butter  @  28? 


6  £6-. 


@  6? 


ct. 
60 

12 
30 
60 
60 


238  PRIMARY   ARITHMETIC 

WRITTEN   EXERCISE 

Copy,  fill,  foot,  and  receipt  each  of  the  following 
bills.  Date  the  bills, 'put  in  the  name,  business,  and 
address  of  some  dealer  you  know,  make  the  bills 
against  yourself,  and  insert  your  address  and  the 
name  of  the  place  ivhere  you  live. 

1. 

[Name  of  place,  and  date} 19 

M [Mr.  or  Miss.    Insert  your  name] [Give  your  address] 

To [Insert  name  of  some  grocer] }  Grocer, 

[Give  his  address] Dr. 

[Date] 2  lb.  Powdered  Sugar  @  1\? $ 

"  2  doz.  Eggs  @  2o/ 

«  \  doz.  Oranges  @  60/ 

[Receipt] $ 


2. 

[Name  of  place,  and  date] 19 

M [Name] [Give  your  address] 

Bought  Of [Name] ,  Grocer, [Give  his  address] 

[Date] 2  heads  of  Lettuce  @  5/ $ 

"  3  lb.  Butter  @  32  / 

"  2  gal.  Oil  @ 

"  4  lb.  Raisins  i 

"  2  lb.  Coffee  i 


[Receipt] 


BILLS   AND   RECEIPTS 


239 


[Name  of  place,  and  date} 19. 

M [Name} 

To [Name} ,  Dealer  in  Meats  and  Poultry, 

[Date} 5  lb.  Eoast  Beef  @  16/ $ 

4  lb.  Chicken  @  22  J/ 

«  6J-  lb.  Lamb  @  20/ 




Dr. 


4. 

[Name  of  place,  and  date} 19 

[Name  of  your  school} 

To [Name} , 

Stationer  and  Bookseller,  Dr. 

[Date} 40  Arithmetics  @  35/ $ 

«  3  doz.  Tablets  @  50/ * 

«  8  doz.  Pencils  @  35/ 

[Receipt} $ 

5. 

[Name  of  place,  and  date} 19 

M [Name} 

Bought  of [Name} ,  Dealer  in  Dry  Goods. 

[Date] 2£  yd.  Flannel  @  $1.00 $ 

"  g£-  yd.  Braid  @  12/ 

«  10  yd.  Embroidery  @  12  J-/ 

"  2  yd.  Taffeta  Silk  @  85X 

[Receipt] $ 

The  teacher  should  encourage  the  pupils  to  inquire  outside  of 
school  about  prices,  so  as  to  make  out  real  bills  of  goods  as  they 
may  be  purchased  in  the  place  where  they  live. 


240  PRIMARY    ARITHMETIC 

WRITTEN   EXERCISE 

Find  the  cost  of  each  of  the  following : 

1.  2  Ib.  tea  @  621X.  2.  3|  Ib.  fish  @  16X. 

3.  If  Ib.  tea  @  48X.          4.  f  Ib.  cocoa  @  64X. 

5.  2f  Ib.  cake  @  32X.        6.  6f  Ib.  figs  @  16X. 

7.  2f  Ib.  dates  @  8X.         8.  2J  Ib.  cereal  ®  8X. 

9.  2|  Ib.  coffee  @  30X.      10.  4J  Ib.  starch  @  8X. 
11.  f  Ib.  pepper  @  32X.     12.  6|  Ib.  prunes  @  8X. 
13.  1|  Ib.  cheese  @  16X.     14.  8  yd.  cloth  @  37  JX. 
15.  If  pt.  catsup  @  20X.    16.  2£  pt.  sirup  @  22X. 
17.  5f  Ib.  raisins  @  32X.    18.  f  Ib.  mustard  @  28X. 
19.  31  Ib.  steak  @  18X.     20.  8|lb.  roast  beef  @16X. 
21.  4f  Ib.  chops  @  16X.     22.  l£lb.  chocolate @40X. 
23.  12yd.calic9@12iX.    24.  3J  qt.  pickles  @  48X. 

25.  3|-  Ib.  walnuts  @  16X. 

26.  3|  Ib.  cocoanut  @  18X. 

27.  1J  Ib.  crackers  @  22X. 

28.  6f  Ib.  mackerel  @  18X. 

29.  f  gal.  olive  oil  @  $2.80. 

30.  21  Ib.  cornstarch  @  10X. 

31.  12|  Ib.  bag  of  flour  @  4X. 

32.  f  Ib.  baking  powder  @  42X. 

33.  5|  Ib.  dried  apricots  @  18X. 

34.  35  cakes  of  soap  @  60  for  $3. 

35.  12  oz.  almonds  @  32X  a  pound. 

36.  2f  Ib.  crystallized  ginger  @  32X. 

37.  2J  qt.  of  chowchow  @  92X  a  gallon. 

38.  ^  Ib.  gelatin  @  9X  per  2-oz.  package. 


REVIEW 


241 


ORAL  EXERCISE 

• 

1.  These  girls  buy  6  cans  of  tomatoes  at  2  cans 
for  a  quarter.     What  do  they  cost? 

2.  What  do  3  Ib.  of  coffee  cost  at  33  ct.  a  pound  ? 

3.  They     buy 
f  Ib.   of   Oolong 
tea   at   48  ct.   a 
pound.     What 
does  that  cost? 

4.  They  buy  11 
Ib.  of  cocoa.  This 
is  56  ct.  a  pound. 
What  does  it  cost? 

5.  They  buy 
J  Ib.   of  allspice 
at  20  ct.  a  pound, 

and  J  Ib.  of  cinnamon  at  40  ct.  a  pound. 
do  these  cost? 

6.  They  also  buy  J  Ib.  of  cheese  at  16  ct.  a  pound, 
and  1  J  Ib.  of  butter  at  30  ct.  a  pound.    How  much 
do  they  pay  for  both? 


What 


WRITTEN  EXERCISE 

1.  Make  out  a  bill  for  the  above  purchases,  fill- 
ing it  out,  footing  it,  and  receipting  it. 

2.  They  find  that  sirup  costs  29  ct.  a  quart,  or 
95  ct.  a  gallon.    If  they  wish  4  qt.,  how  much  will 
they  gain  by  buying  at  the  gallon  rate? 


242 


PRIMARY  ARITHMETIC 


DECIMAL   FRACTIONS 


ORAL   EXERCISE 


?     Then  1  dime 
.10  is  what  part 


1.  How  many  dimes  make 
is  what  part  of  $1?     That  is, 
of  $1? 

2.  How  many  cents  make  $1?     Then  1  cent  is 
what  part  of   $1?     That  is,   $0.01  is  what  part 
of  $1? 

Teachers  should  show  that  just  as  $0.10  is  ^  of  a  dollar,  so 
.10  ft.  is  ^  of  a  foot,  .10  mi.  is  ^  of  a  mile,  and  so  on.  Also 
that  as  $0.01  is  T^  of  a  dollar,  so  .01  yd.  is  T^  of  a  yard. 


3.  In  the  picture,  if  B  is  1, 
what  is  A?   C? 

4.  If  C  is  1,  what  is  B?    A? 

5.  If  A  is  1,  what  is  B?    C? 

6.  If    we    write   A   as    1, 
how  may  we  write  B,  besides 

also  C,  besides  T^? 

We  write  0.1,     or  merely  .1,     for  T^, 
0.01,    «       «       .01,    «  T^ 
and  0.001,  «       «       .001,  «    T^. 

We  also  write  0.5,  or  .5,  for  ^;  0.35,  or  .35,  for 
tffo;  and  8.425  for  Srfftfc 

Fractions  like  .5,  .35,  and  .125  are  called  decimal 
fractions. 

Fractions  like  |,  |,  T6T,  where  the  denominators  are 
written,  are  called  common  fractions. 


DECIMAL   FRACTIONS 


243 


ORAL  EXERCISE 

1.  In  the  picture  point  to  .01  of  the  large  square ; 
to  .25  ;  to  .50  ;  to  .05  ;  to  .10. 

2.  The  large  square  is  how  many 
fourths  of  itself  ?  how  many  thirds 
of   itself?     how   many   tenths    of 
itself?    how  many  hundredths   of 
itself? 

3.  Show  from  the  picture  that  .25  =  ^.     In  the 
same  way,   .75  =  how   many   fourths?     .10  =  how 
many  tenths?    .05  =  how  many  twentieths? 

4.  Study  the  picture  and  name  other  fractions  to 
which  the  following  are  equal : 

.02         .04         .20         .40         .60         .80 

5.  Study  the  picture  and  name  the  decimal  frac- 
tions to  which  these  fractions  are  equal : 


\ 
i 


I 


2*0  2T 

iV  lV 


TO 


WRITTEN    EXERCISE 

1.  Draw  a  square  -Y-  in.  on  a  side,  and  separate 
each  side  into  tenths.    Draw  parallel  lines  dividing 
the  square  into  hundredths,  as  in  the  picture  above. 
Shade  |  of  it,  so  as  to  show  that  -J  =  .20  =  T2¥  =  .2. 

2.  Draw  another  square  like  this  and  shade  33| 
of  the  small  squares,  so  as  to  show  that  ^  =  .33|, 
and  that  f  =  .66*. 

o  o 


244  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  To  what  other  common  fraction  is  ^  equal? 
Then  express  .5  as  a  common  fraction. 

2.  To  what  other  common  fraction  is  T2^-  equal? 
Then  express  .25  as  a  common  fraction. 

3.  How  much  is  .25  of  100?  of  200?  of  400? 

4.  Of  200  pupils  in  a  certain  school,  .25  are  less 
than  12  years  old.     How  many  such  are  there? 

The  name  common  fraction  refers  to  the  way  in  which 
the  fraction  is  written.  Thus,  ^  is  a  common  fraction, 
although  it  is  only  another  way  of  writing  the  decimal 
fraction  .5. 

You  now  see  why  the  period  (.)  after  dollars,  as  in 
$2.50,  is  called  a  decimal  point.  It  separates  the  deci- 
mal fraction  from  the  dollars. 

In  the  number  21,345.789,  we  have 

Periods 
Thousands        Units         Thousandths 


Orders:  gj 

21,345.789 

WRITTEN  EXERCISE 

Write  the  fractions  in  the  following  as  decimal 
fractions  : 

*•  I8o?  T5o?  T2o?  iV  2-  Tihrr-dhr?  Too? 


6.  1^  4Ty&?  $"6TV5o- 


DECIMAL   FRACTIONS  245 

ORAL  EXERCISE 

1.  Express  ^  as  fifths.     Then  .4  =  how  many 
fifths? 

2.  Express  -f$  as   fifths.     Then  .6  =  how  many 
fifths? 

3.  Express  -f$  as  fifths.     Then   .8  =  how  many 
fifths? 

4.  How  many  50's  in  100  ?     Then  express  T5/¥ 
as  halves. 

5.  Because  T5^  =  |,  and  -ffa  =  J,  what  can  you 
say  about  .5  and  .50? 

Annexing  a  zero  to  a  decimal  fraction  does  not  change 
its  value. 

Because  -f$  =  -ffa,  we  see  that  .3  =  .30. 

To  reduce  a  decimal  fraction  to  a  common  fraction, 
write  the  denominator;  then  reduce  to  lowest  terms. 

That  is,  .5  =  T5^,  which  we  see  equals  \  ;  and  *3  =  ^, 
.7=^,.25  =  ^fo  which  is  \. 


WRITTEN  EXERCISE 

1.  Express   %   as   tenths;    then   write   it   as   a 
decimal  fraction.     Express  J  as  tenths;  then  write 
it  as  a  decimal  fraction. 

2.  Write  as  decimal  fractions  : 

&         I  (or  A)          I          A         * 

3.  Write  as  common  fractions  : 

.1         .5         .2         .25         .50         .75 


246  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  Add  $1.20  and  $2.10;  also  1.20  and  2.10. 

2.  Add  $1.50  and  $3;  also  1.5  and  3. 

3.  Add  $4.75  and  $0.25;  also  4.75ft.  and  .25ft. 

4.  Add  $1.30  and  $1.20;  also  1.3  yd.  and  1.2  yd. 

5.  From  $2.50  take  $1.25;  also  from  2.50  mi. 
take  1.25  mi. 

You  have  seen  that  you  add  and  subtract  decimal 

fractions  as  you  do  United  States  money. 

Required  to  add  2.25,  3.2,  and  4.  2.25 

Just  as  we  write  the  decimal  points  in  a  column    3.2 

in  adding  money,  so  we  do  with  decimal  fractions,    4. 

to  add  like  numbers  to  one  another.  9.45 

The  reasons  for  such  operations  can  appear  clear  to  pupils  only 
through  the  efforts  of  the  teacher.  A  text-book  can  give  merely 
a  hint. 

Required  to  subtract  4.25  from  8.2.  8.20 

Since  T2^  is  the  same  as  -f-fa,  the  8.2  may  be  4.25 

written   8.20.     We  may  then  subtract,  as  with  3.95 

United  States  money. 

WRITTEN   EXERCISE 

1.  3.2  +  4.8  +  5.05.         2.  6.4  +  9.35  +  8.2. 
3.  28.42  +  62.4  +  3.9.     4.  7.48  +  5.48  +  6.08. 
5.  39.45-26.25.  6.  47.35-25.05. 

7.  342.8-121.65.  8.  423.45-68.125. 

9.  If  a  table  top  is  3.25  ft.  long  and  1.25  ft.  wide, 
what  is  the  distance  around  it? 


DECIMAL   FRACTIONS  247 

ORAL   EXERCISE 

1.  How  many  10's  in  50?     How  much  is  ^  of 
50?    TWof50?    .10  of  50? 

2.  How  much  is  T^  of  200?     Then  how  much 
isTVoOf200?    .12  of  200?    .11  of  200? 

You  have  seen  that  to  take  .25  of  a  number  you 
may  first  take  .01  and  then  multiply  by  25. 

To  take  .01  of  a  number  like  $350,  we 

$350  $3.ou 

have  seen  that  =  $3.50.     That  is,  in  25 

$350.00  we  move  the  decimal  point  two  1750 

places  to  the  left.  7QO 

That  is,  .25   of  $350  is  found  in  this  $87.50 

way: 

1.  .01  of  $350  =$3.50. 

2.  25  times  $3.50  =  $87.50. 

WRITTEN  EXERCISE 

Multiply  in  Exs.  1-6 : 

1.  $400  by  .20.  2.  $300  by  .75. 

3.  $125  by  .35.  4.  $250  by  .25. 
5.  $425  by  .30.  6.  $630  by  .33f 

7.  In  a  certain  school  of  250  pupils,  .40  of  the 
pupils  were  boys.     How  many  were  boys? 

8.  If  Jack  had  84  marbles  and  lost  .25  of  them, 
how  many  did  he  lose? 

9.  If  Carrie  invited  30  to  her  party  and  .10  of 
them  could  not  come,  how  many  remained  away? 


248  PRIMARY   ARITHMETIC 

KEVIEW  OF  DENOMINATE  NUMBEBS 

ORAL  EXERCISE 

1.  Give  the  table  of  time. 

2.  Give  the  table  of  dry  measure. 

3.  Give  the  table  of  liquid  measure. 

4.  Give  the  table  of  United  States  money. 

5.  Give  the  table  of  length;  of  square  measure; 
of  cubic  measure. 

The  teacher  should  frequently  call  for  the  facts  of  the  various 
tables,  as  well  as  the  tables  themselves.  There  are  advantages  in 
both  of  these  forms  of  drill  work.  The  tables  should  now  be 
thoroughly  known. 

WRITTEN  EXERCISE 

1.  Write  the  table  of  weight. 

2.  Write  the  tables  of  dry  and  liquid  measure. 

3.  Write  the  tables  of  square  and  cubic  measure. 

4.  Write  the  table  of  time,  and  the  names  of 
the  months  having  30  days  each. 

5.  At  70  ct.  a  square  foot,  how  much  will  a  tile 
floor  cost  that  is  3  yd.  wide  and  4  yd.  long? 

6.  If  a  man  gets  40  ct.  an  hour  for  laying  the 
floor,  and  he  works  2  days  at  8  hr.  a  day,  how  much 
does  he  receive? 

7.  Draw  a  plan  of  the  floor  mentioned  in  Ex,  5, 
on  a  scale  of  1  in.  to  the  yard.     Then  measure  the 
number  of  yards  from  one  corner  to  the  opposite 
one.     (The  distance  should  equal  15  ft.) 


DENOMINATE  NUMBERS  249 

ORAL  EXERCISE 

1.  How  many  square  inches  are  there  in  1  sq.  ft.? 
in  1  sq.  ft.  16  sq.  in.? 

2.  How  many  square  feet  are  there  in  1  sq.  yd.? 
in  2  sq.  yd.?   in  2  sq.  yd.  3  sq.  ft.? 

3.  How  far  is  it  around  a  square  that  is  5  ft.  on 
a  side?     What  is  the  area  of  the  square? 

4.  How  long  is  the  side  of  a  square  which  is 
36  yd.  around?  of  one  which  is  40  ft.  around? 

You  already  know  that  144  sq.  in.  =  1  sq.  ft.,  and 
9  sq.  ft.  =  1  sq.  yd.  You  should  now  learn  that 

16O  square  rods  =  1  acre  (A.). 
64O  acres  =  1  square  mile. 

5.  If  a  street  is  4  rd.  wide,  and  you  mark  off 
40  rd.  in  length,  how  many  acres  in  this  part? 

6.  How  many  acres  in  a  street  4  rd.  wide  and 
80  rd.  long?   4  rd.  wide  and  20  rd.  long? 

WRITTEN   EXERCISE 

1.  How  many  square  rods  in  17^-  A.? 

2.  How  many  acres  in  43  sq.  mi.  ?   in  100  sq.  mi.  ? 

3.  A  man  has  a  garden  32  rd.  long  and  15  rd. 
wide.     How  many  acres  does  it  contain? 

The  pupils  should  estimate  40  rd.  in  the  length  of  the  street, 
if  it  is  4  rd.  wide,  so  as  to  see  how  large  an  acre  is.  They  should 
measure  the  school  grounds  and  find  the  area  in  square  rods. 
It  is  also  advantageous  to  measure  an  acre  near  the  school,  so 
as  to  vizualize  this  important  unit. 


250  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

1.  If  each  of  these  bales  of  cotton  weighs. 500  lb., 

how  many 
pounds  does 
the  load  of 
cotton  weigh? 
How  many 
tons? 

2.  If    the 
driver  weighs 

150  lb.,  and  the  wagon  weighs  1200  lb.,  what  is  the 
total  load  these  horses  are  drawing  ? 

3.  If  the  cotton  is  worth  10  ct.  a  pound,  what 
is  the  value  of  each  bale?   of  all  the  bales? 

WRITTEN  EXERCISE 

1.  If  a  bale  of  cotton  weighs  500  lb.,  and  this 
country  produces   10,000,000   bales   a  year,  how 
much  does  one  year's  product  of  cotton  weigh? 

2.  If  this  cotton  is  worth  10  ct.  a  pound,  how 
much  is  the  year's  product  worth? 

3.  If  Texas  produces  .35  of  the  cgtton  in  this 
country,  how  many  bales  are  produced  there  in  a 
year? 

4.  America  produces  five  times  as  much  cotton 
as  the  rest  of  the  world.     At  the  above  rate,  how 
many  bales  does  the  rest  of  the  world  produce? 
How  many  pounds,  at   500  lb.  to  the  bale? 


DENOMINATE   NUMBERS 


251 


ORAL   EXERCISE 

1.  This  boy  has  been  given  an  acre  of  land  for  a 
garden.    It  is  10  rd.  wide.    How  long  is  it?     Draw 
a  plan  on  the  board. 

2.  He  stretched  a  line 
lengthwise  through  the 
middle  of  the   garden. 
How  many  square  rods 
on  each  side? 

3.  He  cut  one  of  the 
two  strips  into  4  plots, 
2  rd.,  2  rd.,  6  rd.,  and 
6  rd.  long.    How  many 
square  rods  in  each? 

4.  He  cut  the  other 
strip  into  5  plots,  2  rd., 

2  rd.,   6  rd.,  3  rd.,  and 

3  rd.  long.    How  many 
square  rods  in  each? 


WRITTEN  EXERCISE 


1.  Draw  a  diagram  of  the  plots,  \  in.  to  1  rd. 

2.  At  2  bu.  to  the  acre,  how  much  seed  did  he 
need  for  the  peas,  the  bed  being  2  rd.  by  5  rd.? 

3.  At  1J  bu.  to  the  acre,  how  much  seed  did  he 
need  for  the  beans,  the  bed  being  2  rd.  by  5  rd.? 

4.  At  8  bu.  to  the  acre,  how  many  bushels  of 
potatoes  did  he  need,  the  bed  being  6  rd.  by  5  rd.? 


252  PRIMARY   ARITHMETIC 

WRITTEN  EXERCISE 

1.  A  mail  bought  a  piece  of  land  near  the  edge 
of  a  village.     The  land  was  50  rd.  long  on  the 
street,  and  16  rd.  deep.      How  many  acres  in  the 
land? 

2.  At  $375  an  acre,  how  much  did  it  cost? 

3.  He  cut  the  land  into  building  lots,  each  5  rd. 
front.     How  many  lots  did  he  have  ?     Draw  a  dia- 
gram of  the  land  showing  the  lots. 

4.  How  many  feet  long  and  wide  was  each  of 
the  building  lots?     What   was  the  area  of  each 
in  square  feet  ?   in  parts  of  an  acre  ? 

5.  He  sold  these  lots  at  $325  each.     How  much 
did  he  gain  on  all  the  land  ? 

6.  A  purchaser  of  one  of  the  lots  put  a  fence 
around  the  three  sides  not  facing  the  street.     The 
fence  cost  $4.50  a  rod.    How  much  did  it  all  cost  ? 

7.  This  same  purchaser  built  a  house  that  cost 
$3258.75,  and  spent   $687.25  for  furniture  and 
$62.50  for  grading.     How  much  did  the  house, 
lot,  grading,  and  fencing  cost? 

8.  If  he  can  save  $750  a  year,  how-  long  will 
it  take  this  purchaser  to  save  enough  to  pay  the 
amount  found  in  Ex.  7  ? 

9.  This   man   built   his   house    3  rd.   from   the 
street,  and  laid  a  4 -ft.  sidewalk  to  his  front  door. 
At  20  ct.  a  square  foot,  how  much  did  this  walk 
cost? 


DENOMINATE  NUMBERS  253 

ORAL   EXERCISE 

1.  A  class  in  cooking  finds  that  a  cup  of  butter 
weighs  8  oz.     How  many  cups  to  the  pound? 

2.  'At  7|-  oz.  to  the  cup,  how  much  do  two  cups 
of  sugar  weigh  ? 

3.  At  8J  oz.  to  the  cup,  how  much  do  two  cups 
of  rice  weigh? 

4.  At  8  oz.  to  the  cup,  how  many  pounds  do 
5  cups  of  milk  weigh? 

5.  At    two   tablespoonfuls    to   the    ounce,   how 
many  tablespoonfuls  of  sugar  to  the  pound? 

WRITTEN  EXERCISE 

1.  For  our  laundry  we  need  3  roller  towels  of 
7^-  yd.  each.    How  many  yards  must  we  purchase? 

2.  The  toweling  costs  12  ct.  a  yard.    How  much 
does  it  all  cost? 

3.  We   bought   2  tubs  at  87£  ct.  each.     How 
much  did  we  pay  for  both?     How  much  for  the 
tubs  and  a  30-ct.  washboard? 

4.  We  bought  2  starch  bowls  at  the  rate  of  8 
for  $1.     How  much  did  the  two  cost? 

5.  The  teakettle  cost  97  ct.,  the  pan  63  ct.,  and 
the  boiler  $1.50.     What  did  the  three  cost? 

6.  What  did  our  4  flatirons  cost  at  37i  ct.  each? 

z 

7.  What  was  the  cost  of  3  packages  of  starch  at 
ct.  a  package,  and  8  cakes  of  soap  at  4J  ct.  each? 

8.  Make  out  a  bill  for  all  of  the  above  items. 


254 


PRIMARY   ARITHMETIC 


WRITTEN  EXERCISE 

Suppose  you  had  a  room  of  your  own,  15  ft.  by  12  ft., 

having  3  windows, 
each  9  ft.  6  in.  high, 
and  could  furnish 
it  just  as  you  wish. 
At  the  stores  you 
find  these  prices : 

Matting,  1  yd. 
wide,  48  ct.  a  yard; 
rugs,  $12.50;  Brus- 
sels carpet,  1  yd. 
wide,  65  ct.  a  yard; 
velvet  carpet,  27  in. 
wide,  $1.10  a  yard; 
easy  chairs,  $3.25; 
desks,  $8.50;  tables, 

$12.00;    bookcases,  $7.50;    sofas,   $11.00;    muslin   for 

curtains,  17  ct.  a  yard. 

1.  Draw  a  plan  on  a  scale  of  \  in.  to  the  foot. 

2.  On  the  plan  show  how  the  strips  of  matting, 
velvet  carpet,  or  Brussels  carpet  would  lie. 

3.  Not  allowing  for  the  fit  of  the  patterns,  how 
many  yards  of  matting  or  Brussels  carpet  would  it 
take  ?  also  of  velvet  carpet  ?    Give  the  cost  of  each. 

4.  If  you  were  to  furnish  the  room  just  as  you 
would  like,  from  the  materials  with  prices  given 
above,  what  would  you  put  into  the  room?     Make 
out  a  bill  for  the  total,  not  forgetting  the  floor, 
curtains,  and  the  furniture. 


DENOMINATE   NUMBERS 


255 


WRITTEN  EXERCISE 


1.  We  have  195,886.9  miles  of  railroad  in  our 
country,  besides  70,105.5  miles  of  second  tracks 
and  sidings.  How  many  miles  of  track  in  all? 


2.  We  have    39,729  locomotives  and  40  times 
as  many  cars.     How  many   cars  have  we  ?     Can 
one  engine  draw  40  cars  ?   40  passenger  cars? 

3.  There  are  27,144  passenger  cars  in  the  coun- 
try.    At  60  persons  to  a  car,  how  many  persons 
could  they  all  carry  at  once? 

4.  On  an  average,  548  people  are  employed  to 
every  100  mi.  of  railroad.     Think  of  some  place 
25  mi.  away,  and  tell  from  this  how  many  people 
are  employed  for  that  distance. 

5.  A   conductor  receives  on  an  average   $3.17 
a  day.     If  he  works  330  days  to  the  year,  how 
much  is  the  average  yearly  salary  ? 

6.  About  how  far  is  it  from  where  you  live  to 
the  nearest  very  large  city  ?     At  3  ct.  a  mile,  how 
much  would  it  cost  a  man  to  go  there?     How 
much  would  it  cost  you,  at  half  fare? 


256 


PRIMARY   ARITHMETIC 


WRITTEN   EXERCISE 


1.  The  canals  more  than  100  mi.  long,  in  this 
country,  are  the  Chesapeake  and  Ohio,  184  mi.; 
Erie,  387  mi. ;  Illinois  and  Michigan,  102  mi. ; 


Lehigh,  108  mi. ;  Miami  and  Erie,  274  mi.;  Morris, 
103  mi.;  Ohio,  317  mi.;  Pennsylvania,  193  mi.;  and 
Schuylkill,  108  mi.  What  is  their  total  length? 

2.  If  3  canal  boatmen  receive  $35.50  apiece  per 
month,  and  1  man  receives  $42.25  and  another 
$45.75,  what  are  the  wages  of  all  five  who  run 
the  boat? 

3.  It   costs   $0.50   a  day  to  feed  each  of   the 
6  mules  that  draw  the  boat  (3  working  at  a  time). 
How  much  does  it  cost  for  foddef  for  a  10-day  trip 
from  Buffalo  to  Albany? 

4.  Of  two  boats  drawn  by  the  same  team,  one 
carries    238.75    tons    of   freight,    and    the    other 
246.75   tons ;    how  much   do  the  two  carry?     If 
they  average  this  amount,  how  much  would  they 
carry  in  the  12  trips  they  make  in  a  year? 


REVIEW  257 


WRITTEN   EXERCISE 

1.  27.4  +  6.27  +  .34.         2.  6.35  +  0.65  +  143. 

3.  3.26 +  .47 +  26.9.         4.  $2.55  +  $3  +"$0.27. 

5.  4.8  +  62.04  +  3.2.          6.  8  ft. +  .8  ft. +  1.2  ft. 

7.  4.09  +  3.01  +  2.9.          8.  17|  ft.  -  9f  ft. 

9.  26.32  in.  -  9  in.  10.  400  ft.  -  89.9  ft. 

11.  67  acres  -  1|  acres.     12.   127.62  in.  -  4.8  in. 
13.  .3  of  $125.  14.  .25  of  $320. 

15.  .331  of  $420.  16.  .75  of  $164. 

17.  .25  of  $1236.  18.  .331  of  $1110. 

19.  .75  of  $3016.  20.  .061  of  $1760. 

21.  2|  times  111  in.  22.  3f  times  $125. 

23.  4|  times  80  yd.  24.  f  of  360  sq.  rd. 

25.  |  of  625  cu.  in.  26.  f  of  1728  cu.  in-. 

27.  60  sq.  ft.  -  .82  sq.  ft.    28.  75.5  mi.  -  6.75  mi. 
29.  42.3  yd.  -  9.23  yd.     30.  40  mi.  -  19.25  mi. 

31.  1276  sq.  in.  -  .27  sq.  in. 

32.  2.3  in.  +  6.8  in.  +  .27  in. 

33.  7yd. +  7.7  yd. +  9.3  yd. 

34.  6  mi.  +  8.9  mi  +  5.65  mi. 

35.  325.4  cu.  ft.  -  87.06  cu.  ft. 

36.  If  2  pencils  cost  5/?  what  will  36  cost? 

37.  If  7  balls  cost  $1.05,  what  will  9  cost? 

38.  If  17  books  cost  $5.10,  what  will  15  cost? 

39.  If  6  yd,  of  carpet  cost  $8,  what  will  5  rcost? 

40.  If  8  bottles  of  ink  cost  72/,  what  will  5  cost? 

41.  If  9  thermometers  cost  $2.43,  what  will  7  cost  ? 

42.  If  f  gal.  of  oil  costs  9X,  what  will  7  gal.  cost? 


258  PRIMARY  ARITHMETIC 

PERCENTAGE 

ORAL  EXERCISE 

1.  How  many  10's  in  40?     How   much  is  ^ 
of  40? 

2.  How  many  50's  in  100?     How  much  is  ^ 
of  100? 

3.  How  many  100's   in   500  ?     How   much   is 
T^  of  500? 

4.  How  much  is  T^T,  or  .01,  of  200?    of  $1? 
of  $2? 

5.  Then  how  much  is  .05  of  200?  of  $1?  of  $2? 

There  is  another  name  for  y^,  or  .01,  besides  one 
one-hundredth.  It  is  one  per  cent. 

One  per  cent  means  the  same  as  one  one-hundredth. 

Two  per  cent  means  the  same  as  two  hundredths. 

Six  per  cent  means  the  same  as  six  hundredths. 

Usually  six  per  cent  is  written  6j&. 

You  should  remember  that  6^,  -jlip  -06,  all  mean 
the  same. 

WRITTEN  EXERCISE 

1.  Write  5y&  as  a  common  fraction;  as  a  decimal 
fraction. 

2.  Write  -ffa  as  a  decimal  fraction;   also  using 
the  sign  °fo. 

3.  Write  .50  as  a  common  fraction;  also  using 
the  sign  J6. 

Classes  which  are  to  continue  in  the  second  book  of  this  series 
may  omit  this  and  the  following  pages. 


PERCENTAGE  259 

ORAL  EXERCISE 

1.  How  much  is  400-100?     Tfo  of  400?     Vf> 
of  400? 

2.  Then  how  much  is  Tfo  of  400?   Vfr  of  400? 
3^  of  400? 

3.  Because  375  + 100  =  3TV5«,  or  3.75,  Vf>  of  375 
is  how  many? 

4.  Then  how  much  is  IJb  of  240?   of  465?   of 
535?  of  762?  of  850? 

5.  Then  how  do  you  easily  find  1/fc  of  a  number? 

To  find  I'jo  of  a  number,  place  a  decimal  point  to  the 
left  of  tens. 
That  is, 

IJfc  of  425  is  4.25,  because  425  -s-  100  =  4.25; 
1J6  of  $352  is  $3.52,  because  $352  -*- 100  =  $3.52; 
\<jo  of  24.5  is  .245,  because  24.5  -s- 100  =  .245. 

6.  How  much  is 

1%  of  |240?      1%  of  $370?  1%  of  $4200? 

1%  of  $475?      1%  of  $225?  1%  of  $6325? 

1%  of  25.5?        1%  of  $35.30?  1%  of  $426.50? 

7.  By  what  must  you  multiply  Ifi  to  get  5^>? 
How  much  is  Vjo  of  $200?     How  much  is  5$fe  of 
$200? 

8.  How  much  is 

6%  of  $200?  4%  of  $500?  3%  of  $400? 
2%  of  $1000?  3%  of  $100?  5%  of  $300? 
3%  of  $6000?  8%  of  $200?  7%  of  $500? 


260  PRIMARY   ARITHMETIC 

You  have  now  found  that  to  take  6  °/0  of  a  number 
you  may  first  take  1%,  by  dividing  by  100,  and  then 
multiply  by  6.  Other  per  cents  are  found  in  the  same 
way. 

Required  to  find  8%  of  $642.  $642 

1%  of  $642  =  $6.42,  and  8%  of  $642  =  8       $6.42 

times  $6.42,  or  $51.36. 

$51.36 

WRITTEN   EXERCISE 

In  Exs.  1-10  find  the  per  cents  stated: 

1.  5^  of  $425.  2.  6^  of  $750. 

3.  3#  of  $250.  4.  4^  of  $800. 

5.  6^  of  $370.  6.  8#  of  $420. 

7.  10/o  of  $275.  8.  12#  of  $550. 

9.  6J#  of  $500.  10.  12^  of  $400. 

11.  Out  of  a  school  of  250,  0>fi  are  sick.     How 
many  are  sick? 

12.  Out  of  a  class  of  50,  10^  failed  to  be  pro- 
moted.    How  many  failed? 

13.  Out  of  a  school. of  200,  55^  are  girls.     How 
many  are  girls?     How  many  are  boys? 

14.  A   30-ft.  fish  line   shrinks   5^  on  being  put 
into  water.     How  much  does  it  shrink? 

15.  A  250-ft.  kite  string  shrinks  3^  after  being 
out  in  the  rain.     How  much  does  it  shrink? 

16.  If    you    have    82/fe    in   spelling,   how   many 
words  did  you  spell  correctly  out  of  100?   out  of 
50?'    If  you  have  90fo  in   arithmetic,  how  many 
questions  did  you  answer  correctly  out  of  10? 


DISCOUNTS  261 

DISCOUNTS 

ORAL  EXERCISE 

1.  At  a  bargain  sale  a  dealer  offers  a  $2  sled 
at  lOJfc  off.     How  much  is  it  reduced  in  price? 

2.  He  offers  a  50-ct.  knife  at  20/o  off.     How 
much  is  it  reduced  in  price  ?     (20Jfe  =  -f^  =  ^.) 

3.  A  fishing  rod  is  marked  $2.50,  but  he  offers 
it  at  20/o  off.     How  much  does  it  then  cost  ? 

4.  A  dealer  offers  a  $10  suit  at  Wfi  off.     What 
is  the  price  now? 

5.  Your  book  dealer  buys  $40  worth  of  books 
at  20/fe  off.     How  much  does  he  pay  for  them? 

A  reduction  made  in  the  marked  price  of  goods  is 
called  a  discount. 

Discounts  are  usually  reckoned  in  per  cent. 
The  discount  on  $350  worth  of  goods  at  20%,  and 
the  cost,  are  found  thus : 

20%  of  $350  =  $70,  discount. 
$350  -  $70  =  $280,  cost. 

WRITTEN  EXERCISE 

Find  the  discount  and  cost  of  the  following: 

1.  $250  worth  of  goods  at  25/o  discount. 

2.  $320  worth  of  goods  at  15^  discount. 

3.  $440  worth  of  goods  at  12^  discount. 

4.  $225  worth  of  goods  at  33/o  discount. 

5.  A  $12  suit  of  clothes  at  20fo  discount. 

6.  A  $30  set  of  furniture  at  33£Jfe  discount. 


262  PRIMARY   ARITHMETIC 

INTEREST 
ORAL  EXERCISE 

1.  How  much  is  4%  of  $50? 

2.  How  much  is  5%  of  $200? 

3.  How  much  Is  6%  of  $300? 

4.  How  much  is  3%  of  $120? 

When  a  man  borrows  money  he  pays  for  it  by  a  cer- 
tain per  cent  of  the  amount  borrowed. 

The  money  paid  for  the  use  of  other  money  is  called 
interest. 

If  the  interest  is  6%  a  year,  a  man  would  pay  for  the 
use  of  $200, 

6%  of  $200,  or  $12,  if  he  kept  it  a  year; 
£  of  6%  of  $200,  or  $6,  for  \  year,  or  6  mo.; 
\  of  6%  of  $200,  or  $4,  for  \  year,  or  4  mo. ; 
2  times  6%  of  $200,  or  $24,  for  2  years. 
How  much  is  the  interest  on  $350  for  8  mo.  at  4% 
per  year? 

4%  of  $350  =  $14,  interest  for  one  year; 
8  mo.  =  -f%  of  a  year,  or  |  of  a  year ; 
f  of  $14  =  $9.33,  interest  for  f  yr. 

WRITTEN  EXERCISE 

Find  the  interest  on  the  following : 

1.  $300  for  1  yr.  at  6%  per  year. 

2.  $400  for  2  yr.  at  5%  per  year. 

3.  $125  for  6  mo.  at  4%  per  year. 

4.  $375  for  3  yr.  at  4^  per  year. 


INTEREST  263 

WRITTEN  EXERCISE 

Find  the  interest  on  the  following  : 

1.  $200  for  4  yr.  at  5#. 

2.  $350  for  2  yr.  at  6/0. 

3.  $250  for  3  yr.  at  4J&. 

4.  $400  for  li  yr.  at  5fr 

5.  $100  for  9  mo.  at  6Jb. 

6.  $50  for  1  yr.  at  5#. 

7.  $75  for  6  mo.  at  4#. 

8.  $50  for  8  mo.  at  6/0. 

9.  $250  for  6  mo.  at  5#. 

When  money  is  borrowed  the  written  promise  to 
pay  it  back  again  is  called  a  promissory  note.  A  prom- 
issory note  usually  reads  like  this  : 

$200  @Al<WU}0-,   Jll.,   [Dale]  ............ 

,  wuyntA& 
to-  ba,u  to 


at 


10.  Make  out  and  sign  a  promissory  note  for 
$50,  payable  to  the  order  of  John  X.,  in  6  mo., 
with  interest  at  6/0.     Then  find  the  interest. 

11.  Also  one  to  the  same  man,  for  $100,  due 
in  3  mo.,  with  interest  at  5^.     Find  the  interest. 

12.  Also  one  to  the  same  man,  for  $200,  due  in 
1  yr.,  with  interest  at  4fo.     Find  the  interest. 


264  PRIMARY   ARITHMETIC 

WRITTEN   EXERCISE 

1.  469  +  289  +  73.4.         2.  6825  + .71  +  7.29. 

3.  12,407-8798.  4.  21,000-16,725. 

5.  $4283-$275.50.  .  6.  $683.50  -  $217.75. 

7.  147J  ft.  -  68f  ft.          8.  623.|  yd.  -  87f  yd. 

9.  64  x  62  x  8f  10.  825  x  175  x  14. 

11.  175  x  23  x  60.  12.  2x3x4x5x6. 

13.  82 1  times  475.  14.  68£  times  488. 

15.  54|  times  $48.  16.  24|  times  $39. 

17.  7395-435.  18.  $75  +  125. 

19.2668  +  116.  20.2951-227. 

21.  7650-340.  22.  3780-120. 

23.  $6.25-125.  24.  $630-150. 

25.  TV  of  221-  ft.  26.  13,875  -  125. 

27.  $2670-240.  28.  61,206-606. 

29.  22,725  -  225.  30.  &  of  87|  cu.  in. 

Express  as  common  fractions: 
31.   .64.       32.   .36.     33.   .85.      34.   .55.     35.   .90. 
36.  .66.      37.  .16.     38.  .37.      39.  .62.     40.  .87. 

Express  as  decimal  fractions  or  as  lohole  num- 
bers and  decimals : 

41.  f .       42.  f        43.  TV        44.  TV        45.  f 
46.  2f     47.  3|.     48.   5Tfo.  49.  -7tfo.  50.   9^- 

51.  Kow  much  is  16%  of  $240?  of  $175?   of 
$325?  of  $450?  of  $1200?  of  $2575?  . 

52.  At  33f  %  discount,  what  will  an  $18''suit  of 
clothes  cost?  a  $27.75  suit? 


DECIMAL   FRACTIONS  265 


DECIMAL  FRACTIONS  CONTINUED 

Because  3^  =  ±/-  (page  224),  therefore 
.3^  =  -3^°-  -r- 10  =  |.     In  the  same  way,  12 J  = 

^  1       1    • '  25          25         1 

and    .12^  =  77777  of  —  = 

z> 


0    100 


ORAL    EXERCISE 

Reduce  to  common  fractions : 

1.  21,    .21.            2.  11,    .If  3.  31,    .31. 

4.  41,    .41             5.  31,    .31.  6.  41,     .41. 

7.  31,  .031.            8.  21,  .021.  9.  2J,  .02}. 

10.  2{,  .02f           11.  5i,  .051.  12.  31,  .031. 

Express  as  cents: 
13.  $0.2i.      14.  |o.3i.      15.  $0.51.      16.  $0.31. 

In    Ex.  16  we  have  3  dimes  and  ^  of  a  dime. 
17.   $0.2f      18.   $0.71.      19.   $0.51.      20.   $1.21. 

WRITTEN   EXERCISE 

•     Reduce  to  common  fractions  : 

1.  .121.     2.  .321.      3.  .41^.     4.  .261.  5.  .221. 

6.   .66}.      7.  .331.      8.   .371.      9.  .621.  IQ.   .871. 

11.  .02f    12.   .03}.    13.   .05}.    14.  .07f  15.   .111. 
16.  .77f    17.  .28f    18.  .56}.    19.  .48}.  20.  .69f 

Express  as  per  cents,  using  the  sign  %  : 

21.   .23.      22.   .42.      23.  .75.      24.   .62.      25.  .41. 

26.   .2.         27.   .3.         28.   .5.         29.   .7.        30.  .8. 

31.   .21.      32.   .31.      33.  .51.      34.   .7J.      35.  .81. 


266 


PRIMARY   ARITHMETIC 


EEVIEW    OF   PEIMAEY  ARITHMETIC 

If  desired  this  review  may  be  taken  immediately  after 
the  indicated  parts  of  the  book  have  been  studied. 

REVIEWING  PAGES  32-50 

ORAL    EXERCISE 

In  each  column  add  the  numbers  to  the  right  of 
1.  A  and  B.     2.  B  and  C. 
3.  CandD.     4.  DandE. 
5.  EandF.     6.  F  and  G. 

In  each  row  add  the  num- 
bers below 

7.  I  and  II. 

8.  II  and  III. 

9.  Ill  and  IV. 

10.  IV  and  V.      11.  V  and  VI.      12.  VI  and  VII. 

WRITTEN   EXERCISE 

In  each  column  add  the  numbers  to  the  right  of* 
1.  AandB.     2.  B  and  C. 

3.  C  and  D.  4.  D  and  E. 

5.  E  and  F.  6.  A  to  C. 
7.  B  to  D.       8.  C  to  E. 

9.  D  to  F.  10.  A  to  D. 

11.  B  to  E.  12.  C  to  F. 
13.  A  to  E.  u.  B  to  F. 

15.  A  to  F. 


I 

II 

111 

IV 

V 

VI 

VII 

A 

62 

7 

20 

9 

30 

8 

31 

B 

3 

21 

8 

30 

7 

62 

7 

C 

47 

2 

53 

6 

22 

3 

42 

D 

2 

45 

4 

41 

5 

94 

5 

E 

25 

4 

70 

8 

41 

4 

34 

F 

4 

33 

6 

21 

1 

32 

6 

G 

36 

2 

44 

6 

33 

7 

44 

I 

II 

III 

IV 

V 

VI 

VII 

A 

1 

27 

30 

20 

1 

10 

10 

B 

0 

11 

25 

30 

3 

10 

20 

C 

10 

10 

1 

3 

0 

32 

33 

D 

32 

0 

2 

1 

20 

24 

0 

E 

43 

1 

0 

15 

10 

10 

10 

F 

2 

12 

31 

30 

4 

0 

10 

REVIEW 


267 


ORAL    EXERCISE 

In  each  column  state  the  difference  betiveen  the  two 
numbers  to  the  right  of 
1.  AandB.     2.  BandC. 
3.  C  and  D.     4.  D  and  E. 
5.  EandF.     6.  FandG. 

In  each  row  state  the 
difference  between  the  two 
numbers  below 

7.  I  and  II. 

8.  II  and  III. 

9.  Ill  and  IV. 
11.  V  and  VI. 


I 

II 

III 

IV 

V 

VI 

VII 

A 

98 

96 

95 

85 

74 

64 

52 

B 

87 

74 

64 

53 

53 

52 

40 

C 

65 

54 

44 

43 

42 

30 

20 

D 

42 

22 

22 

21 

20 

10 

9 

E 

21 

20 

10 

10 

9 

9 

7 

F 

10 

10 

5 

4 

2 

1 

1 

G 

5 

3 

3 

2 

2 

1 

0 

10.  IV  and  V. 
12.  VI  and  VII. 


WRITTEN   EXERCISE 

In  each  column  write  the  difference  between  the 
two  numbers  to  the  right  of 
1.  AandB.     2.  BandC. 
3.  CandD.     4.  D  and  E. 
5.  EandF.     6.  FandG. 
7.  AandC.     8.  AandD. 
9.  AandE.  10.  AandF. 

In  each  row  write  the 
difference  between  the  two 
numbers  below 
11.  I  and  II.  12.  II  and  III.  13.  Ill  and  IV. 
14.  IV  and  V.  15.  V  and  VI.  16.  VI  and  VII. 
17.  I  and  III.  18.  I  and  IV.  19.  I  and  V. 


_ 

I 

II 

III 

IV 

V 

VI 

VII 

A 

98 

86 

86 

66 

54 

32 

"22" 

B 

87 

84 

76 

55 

24 

21 

20 

C 

85 

72 

65 

33 

23 

11 

9 

D 

74 

61 

51 

31 

21 

9 

6 

E 

63 

40 

40 

20 

11 

7 

4 

F 

60 

30 

20 

15 

10 

6 

2 

G 

40 

30 

10 

8 

7 

5 

0 

268  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  If  I  add  24  to  30,  what  is  the  result? 

2.  What  number  added  to  24  will  make  68? 

3.  What  number  taken  from  79  will  leave  52? 

4.  If  I  take  half  of  60  from  60,  what  remains? 

5.  If  I  add  40  to  half  of  40,  what  is  the  result? 

6.  Make  a  problem,  using  30  ct.,  5  ct.,  and  2  ct. 

7.  There  are  67  books  on  a  shelf.     All  except 
35  are  new.     How  many  are  new? 

8.  If  a  boy  missed  6  words  in  a  spelling  lesson 
of  29  words,  how  many  did  he  spell  correctly? 

9.  Mary  has  24  red  roses  and  half   as   many 
white  ones.     How  many  white  ones  has  she? 

10.  It  takes  James  10  minutes  less  than  half  an 
hour  to  come  to  school.     How  many  minutes  does 
it  take  him? 

11.  If  a  teacher  is  standing  12  ft.  from  one  side 
of  the  room  and  17  ft.  from  the    opposite  side, 
how  wide  is  the  room? 

12.  In  a  basket  are  a  dozen  eggs.     If  we  add  a 
fourth  of  a  dozen  and  also  a  third  of  a  dozen,  how 
many  eggs  will  there  be? 

13.  There  are  93  pages  in  Chapters  I  and  II  of 
this  book.     When  you  have  finished  page  50,  how 
many  pages  are  left  before  Chapter  III? 

14.  Martha  has  a  dime  and  2  nickels.     If  she 
spends  3  ct.  at  one  store  and  buys  a  2-ct.  postage 
stamp,  how  many  cents  will  she  have  left? 


REVIEW  269 


WRITTEN   EXERCISE 

1.  How  far  is  it  around  a  room  20  ft.  long  and 
14  ft.  wide? 

2.  What  number  added  to  |  of  40  equals  15? 
equals  20?  equals  23? 

3.  Make  a  problem  about  ^  of  60 ;  about  |  of 
80 ;  about  £  of  40 ;  about  £  of  30. 

4.  Frank  has  a  book  of  75  pages.     He  has  read 
32  pages.     How  many  has  he  still  to  read? 

5.  On  a  railway  journey  of  86  miles  how  many 
miles  are  left  after  a  man  has  gone  12  miles? 

6.  There  are  12  boys  in  one  row,  6  in  another, 
and  4  in  another.     How  many  in  all  three  rows? 

7.  On  a  page  containing  40  problems  Frank 
solved  all  but  £.     How  many  did  he  solve? 

8.  Ruth  had  28  ct.,  and  spent  15  ct.  for  paper 
and  pencils.    Her  father  then  gave  her  10  ct.    How 
much  did  she  then  have? 

9.  The  first  day  of  school  Rose  spent  44  ct.  for 
books,  12  ct.  for  paper,  5  ct.  for  a  pencil,  and  paid 
a  nickel  for  car  fare.     How  much  did  she  spend? 

10.  Charles  had  24  ct.  in  his  bank  on  Monday. 
He  put  in  12  ct.  on  Tuesday,  10  ct.  on  Wednesday, 
and  2  ct.  on  Thursday.     How  much  had  he  then? 

11.  There  were  12  birds  on  a  tree  and  14  on  the 
ground.     Four  birds  flew  from  the  ground  to  the 
tree.     How  many  more  were  then  on  the  tree  than 
on  the  ground? 


270  PRIMARY  ARITHMETIC 

KEVIEWING  PAGES  51-93 
ORAL   EXERCISE 

1.  How  many  feet  in  7  yd.  and  2  ft.? 

2.  How  many  days  in  4  wk.  and  6  da.? 

3.  At  3  for  a  dime,  what  will  12  apples  cost? 

4.  If  one  hat  costs  $2,  what  will  20  hats  cost? 

5.  If  a  book  costs  30  ct.,  what  will  3  books  cost? 

6.  Edward  weighs  52  Ib.  8  oz.,  and  Mary  weighs 
42  Ib.  4  oz.     What  do  both  together  weigh? 

7.  Henry  has  a  peck  of  nuts  and  2  qt.  over.    If 
he  sells  them  at  5  ct.  a  quart,  what  will  he  get? 

8.  If  a  wheel  goes  7  feet  every  time  it  turns, 
how  many  yards  does  it  go  in  turning  three  times? 

9.  When  Richard  drives  3  miles  he  has  gone  ^ 
of  the  distance  to  his  aunt's  home.    How  far  is  it 
to  his  aunt's  home? 

10.  If  the  last  chapter  of  a  book  is  XIX,  and 
you  are  at  the  beginning  of  Chapter  XI,  how  many 
chapters  have  you  yet  to  read? 

11.  Fred  sold  some  berries,  making  2  ct.  on  each 
quart.    He  sold  12  qt.  one  day  and  20  qt.  the  next 
day.    How  much  did  he  make  ? 

12.  A  dealer  pays  12  ct.  a  gallon  foAnilk  and 
sells  it  at  6  ct.  a  quart.     How  much  does  he  make 
on  a  quart?  on  a  gallon?  on  2  gallons? 

13.  If  you  buy  4  Ib.  of  meat  at  9  ct.  a  pound, 
how  much  does  it  cost?     If  you  pay  for  it  with  a 
half  dollar,  what  change  should  you  receive? 


REVIEW  271 

WRITTEN   EXERCISE 

Add  the  following ',  timing  yourself: 

1.  $217   2.  246yd.  -3.  276ft.   4.  329  in.     5.  $437 
343        434  427  286  293 


6. 

$127 

7.  142yd. 

8.  326  ft. 

9.  463  in. 

10.  $123 

246 

237 

293 

298 

247 

329 

421 

147 

127 

409 

11. 

106 

12.  213 

13.  106 

14.  132 

15.  222 

287 

129 

219 

167 

333 

109 

308 

137 

207 

111 

300 

127 

204 

122 

107 

114 

.135 

317 

109 

112 

16. 

121 

17.  106 

18.  217 

19.  272 

20.  319 

42 

92 

102 

129 

107 

37 

37 

69 

106 

28 

168 

15 

72 

43 

63 

29 

208 

31 

16 

29 

343 

319 

427 

121 

142 

21. 

$136 

22.  $127 

23.  $147 

24.  $192 

25.  $400 

42 

38 

29 

37 

125 

81 

25 

108 

91 

30 

92 

172 

32 

82 

19 

237 

81 

129 

263 

16 

148 

69 

70 

109 

128 

129 

232 

63 

78 

37 

272  PRIMARY   ARITHMETIC 

WRITTEN  EXERCISE 

Subtract,  timing  yourself: 


1. 

5. 
9. 
13. 
17. 
21. 
25. 

236 
129 

2. 
6. 
10. 
14. 
18. 
22. 
26. 

342 

273 

3. 

7. 
11. 
15. 
19. 
23. 
27. 

409 
263 

4. 
8. 
12. 
16. 
20. 
24. 
28. 

527 
329 

400 
192 

326 

178 

409 
237 

600 

482 

725 
536 

908 
809 

752 
429 

360 

290 

728 
299 

342 
139 

801 
236 

712 

348 

801 

296 

902 

327 

711 

344 

628 
439 

$426 
278 

$304 
265 

$322 
148 

$209 
168 

$387 
296 

$400 

275 

$925 
560 

$305 
197 

29.  492ft.  30.  286ft.  31.  840yd.  32.  927ft. 
137                 192                726  109 

33.  209  bu.  34.  325  bu.  35.  430ft.  36.  535  bu. 
110                 186                 345  287 

37.  520ft.  38.  480ft.  39.  322ft.  40.  400ft. 
137                 196                 192  229 


REVIEW  273 


ORAL  EXERCISE 

1.  2x1  +  1. 

2.  2x2  +  1. 

3.  2x3  +  1. 

4.  2x4  +  1. 

5.  2x5  +  1. 

6.  3x1  +  1. 

7.  3x2  +  1. 

8.  3x3  +  1. 

9.  3x4  +  1. 

10.  3x5  +  1. 

11.  3x1  +  2. 

12.  3x2  +  2. 

13.  3x3  +  2. 

14.  3x4  +  2. 

15.  3x5  +  2. 

16.  4x1  +  1. 

17.  4x2  +  1. 

18.  4x3  +  1. 

19.  4x4  +  1. 

20.  4x5  +  1. 

21.  4x1  +  2. 

22.  4x2  +  2. 

23.  4x3  +  2. 

24.  4x4  +  2. 

25.  4x5  +  2. 

26.  4x1  +  3. 

27.  4x2  +  3. 

28.  4x3  +  3. 

29.  4x4  +  3. 

30.  4x5  +  3. 

31.  5x1  +  1. 

32.  5x2  +  1. 

33.  5x3  +  1. 

34.   5x4  +  1. 

35.  5x5  +  1. 

36.   5x1  +  2. 

37.  5x2  +  2. 

38.  5x3  +  2. 

39.  5x4  +  2. 

40.  5x5  +  2. 

41.  5x1  +  3. 

42.  5x2  +  3. 

43.  5x3  +  3. 

44.  5x4  +  3. 

45.  5x5  +  3. 

46.  5x1  +  4. 

47.  5x2  +  4. 

48.  5x3  +  4. 

49.  5x4  +  4. 

50.  5x5  +  4. 

51.  5x5  +  5. 

WRITTEN  EXERCISE 

Multiply,  timing  yourself: 

1.  32       2.  29 

3.    47           4.    53 

5.  65       6.  61 

_2           _3 

-i                  _§ 

_!        _J> 

7.  62       8.  26 

9.  36      10.  63 

11.  66     12.  73 

_!           _§ 

_2            _4 

_5             6 

13.  27     14.  63 

15.  54.     16.  45 

17.  43     18.  39 

5             4 

3             2 

4             5 

274  PRIMARY   ARITHMETIC 

ORAL   EXERCISE 

1.  At  $32  each,  what  do  2  cows  cost? 

2.  At  $33  each,  what  do  3  cows  cost? 

3.  At  $12  each,  what  do  3  tables  cost? 

4.  At  $60  each,  what  do  2  horses  cost? 

5.  At  $20  a  month,  what  is  4  months'  rent? 

6.  At  $22  a  dozen,  what  do  3  doz.  hats  cost? 

7.  At  $24  a  dozen,  what  do  2  doz.  lamps  cost? 

8.  At  $34  a  set,  what  do  2  sets  of  furniture  cost? 

9.  At  $42  an  acre,  what  do  2  acres  of  land  cost? 

10.  At  $40  an  acre,  what  do  3  acres  of  land  cost  ? 

11.  At  $30  a  dozen,  what  do  4  dozen  chairs  cost? 

12.  At  $30  a  set,  what  do  4  sets  of  furniture  cost? 

13.  At  $20  a  suit,  what  do  5  suits  of  clothes  cost? 

14.  Mary  has  22  ct.  and  Kate  has  1  ct.  less  than 
twice  as  much.     How  much  has  Kate  ? 

15.  William  has  14  ct.  and  John  has  1  ct.  more 
than  twice  as  much.     How  much  has  John  ? 

WRITTEN  EXERCISE 

Multiply.,  timing  yourself: 


1. 

32 

2. 

49 

3. 

76 

4. 

58 

5. 

19 

6. 

82 

_5 

_2 

3 

4 

_5 

_5 

7. 

27 

8. 

33 

9. 

47 

10. 

86 

11. 

29 

12. 

64 

4 

_5 

_2 

J 

j5 

_3 

13. 

48 

14. 

29 

15. 

38 

16. 

44 

17. 

23 

18. 

39 

4 

3 

2 

4 

5 

3 

REVIEW  275 

ORAL   EXERCISE 

1.  How  many  3's  in  15?  6?  21?  9?  27?  12?  30? 

2.  How  many  2's  in  6?  4?  8?  2?  14?  20?  16? 

3.  How  many  4's  in  16?  20?  4?  36?  8?  40? 

4.  How  many  5's  in  5?  50?  10?  45?  20?  15? 

5.  4)16.    6.  4)24.    7.  3)36.    8.  2)18. 
9.  5)35.   10.  2)22.   11.  3)27.   12.  5)55. 

13.  2)18.   14.  3)27.   15.  4)36.   16.  3)40. 

17.  At  $4  each,  how  many  hats  will  $28  buy? 

18.  At  $2  each,  how  many  sleds  will  $20  buy? 

19.  At  $4  each,  how  many  desks  will  $44  buy? 

20.  At  $3  each,  how  many  books  will  $24  buy? 

21.  At  $5  each,  how  many  sheep  will  $35  buy? 

22.  At  $3  each,  how  many  lamps  will  $30  buy? 

23.  At  $2  each,  how  many  chairs  will  $18  buy? 

24.  At  $5  each,  how  many  tables  will  $35  buy? 

25.  At  $3  each,  how  many  stands  will  $27  buy? 

WRITTEN   EXERCISE 

1.  3)336.      2.  4)444.     3.  3)936.      4.  5)555. 

5.  3)369.      6.  3)633.      7.  4)848.      8.  2)806. 

9.  4)804.    10.  5)500.    11.  3)699.     12.  2)208. 

13.  3)306.    14.  4)840.     15.  2)824.     16.  4)888. 

17.  At  $3  each,  how  many  books  will  $69  buy? 

18.  At  $5  each,  how  many  tables  will  $550  buy? 

19.  At  $4  each,  how  many  desks  will  $404  buy? 
2Q.  At  $4  each,  how  many  lamps  will  $484  buy? 
21.  At  3  ct.  each,  how  many  pencils  will  96  ct.buy? 


276  PRIMARY    ARITHMETIC 

RE  VIEWING  PAGES  94-128 

ORAL   EXERCISE 

Add  from  the  bottom  to  the   top,  checking   the 
result  by  adding  from  the  top  to  the  bottom: 

1.  3  2.  9  3.  2  4.  5  5.  6  6.  8  7.  2  8.  5 
22888283 
43732338 
67385462 
5642  5"  796 
75997689 
98633278 
32892943 

These  are  types  of  problems  to  be  written  on  the  board  for 
rapid  drill  work. 

WRITTEN  EXERCISE 

Add,  checking  as  stated  above : 


1. 

23 

2.  89 

3.  37 

4.  85 

5.  81 

48 

64 

40 

23 

72 

72 

73 

29 

40 

35 

69 

29 

82 

27 

86 

43 

82 

76 

82 

92 

6. 

128 

7.  834 

8.  823 

9.  828 

10.  348 

932 

281 

204 

926 

492 

486 

342 

896 

349 

687 

529 

907 

480 

877 

402 

348 

602 

320 

492 

374 

726 

270 

981 

681 

200 

REVIEW  277 

11.  $127.50  12.  $128.40  13.  $282.00  14.  $375.25 


29.60 

134.00 

127.00 

42.80 

32.80 

29.86 

35.98 

6.75 

142.70 

41.75 

21.76 

0.27 

36.00 

234.60 

142.82 

13.42 

42.75 

12.42 

39.50 

23.61 

31.42 

314.73 

236.45 

180.00 

11.35 

15.92 

37.50 

17.65 

21.07 

26.70 

29.48 

32.80 

In  Exs.  15  '-2  '2,  check  each  result  by 

adding  the 

sum  of  the  first  four  numbers 

to  the  sum 

of  the  last 

four  : 

15.  $134.48  16. 

$125.50  17. 

$298.73   is.  $372.82 

29.64 

29.72 

42.81 

600.25 

9.27 

134.00 

168.00 

408.30 

3.05 

286.75 

425.50 

270.09 

28.06 

120.00 

209.08 

62.85 

42.71 

23.45 

700.00 

131.96 

296.32 

8.20 

63.75 

29.72 

38.00 

19.62 

41.50 

37.00 

19.  $162.82  20. 

$628.75  21. 

$342.98  22.  $826.49 

63.48 

42.96 

172.86 

298.39 

41.79 

134.82 

49.83 

827.63 

29.63 

148.96 

128.49 

294.81 

128.34 

273.48 

23.67 

372.42 

263.98 

107.62 

42.91 

862.84 

471.26 

34.81 

87.08 

981.96 

29.42 

29.62 

231.00 

286.43 

278  PRIMARY    ARITHMETIC 

ORAL   EXERCISE 

1.  How  many  2's  in  2?  4?  8?  16?  20?  22? 

2.  How  many  2's  in  3, -and  what  remainder?  in 
9?  7?  11?  17?  21?  15?  23?  13?  25?  19?  31?  41? 

3.  How  many  3's  in  4,  and  what  remainder?  in 
7?  8?  31?  10?  16?  22?  17?  19?  13?  15?  23?25? 

4.  4)5.  5.  4)_6.  6.  4)7.          7.  4)9. 

8.  4)11.          9.  4)13.        10.  4)15.       11.  4)17. 

12.  4)21.        13.  4)22.        14.  4)23.       15.  4)25. 

16.  5)16.        17.  5)18.        18.  5)21.       19.  5)23. 

20.  5)29.        21.  5)32.        22.  5)34.       23.  5)37. 

24.  6)25.        25.  6)28.       26.  6)32.       27.  6)34. 

28.  6)49.  29.  6)52.  30.  6)56.  31.  6)63. 
32.  7)25.  33.  7)29.  34.  7)34.  35.  7)39. 
36.   7)48.  37.  7)52.  38.  7)58.  39.  7)60. 
40.  8)25.  41.  8)29.  42.  8)31.  43.  8)35. 
44.  8)42.  45.  8)45.  46.  8)50.  47.  8)55. 
48.  9)23.  49.  9)38.  50.  9)42.  51.  9)50. 

WRITTEN   EXERCISE 

1.  6)1234.    2.  5)1264.    3.  3)2986.    4.  4)3682. 

5.  2)3333.    6.  4)1265.     7.  5)8213.    8.  4)2807. 

9.  7)2120.  10.  7)3142.  11.  7)6283.  12.  8)2840. 

13.  6)3042.  14.  6)2187.  15.  8)3190.  16.  9)8142. 

17.  9)2130.  18.  9)2640.  19.  9)81.80.  20.  7)8263. 

21.  5)6666.  22.  4)2343.  23.  5)4444.  24.  6)4002. 

25.  4)1763.  26.  5)8100.  27.  2)7777.  28.  3)4007. 

29.  4)7373.  30.  8)9119.  31.  9)9074.  32.  8)6606. 


REVIEW  279 


WRITTEN   EXERCISE 

1.  At  3  ct.  a  cake,  what  do  2  doz.  cakes  of  soap 
cost?     How  much  change  is  due  out  of  $1? 

2.  At  8  ct.  a  pound  for  rice  and  5  ct.  a  pound 
for  tapioca,  how  much  will  8  Ib.of  each  cost? 

3.  At  5  ct.  a  pound,  what  do  16  Ib.  of  sugar 
cost?    How  much  change  is  due  out  of  $1? 

4.  At  16  ct.   a  pound,  what  does  a  2-lb.  cake 
cost?     How  much  change  is  due  out  of  50  ct. ? 

5.  At  3  ct.  a  loaf,  how  much  must  a  dealer  pay 
a  baker  for  23  loaves  of  bread?    If  the  dealer  sells 
the  bread  at  5  ct.  a  loaf,  how  much  does  he  gain  ? 

6.  Margaret  bought  2  Ib.  of  raisins  at  35  ct.  a 
pound,   and  a   gallon  of   maple   sirup   for   $1.15. 
She  gave  the  grocer  $2.     What  change  was  due? 

7.  If  a  box  of  starch  costs  57  ct.  and  a  bag  of 
flour  costs  88  ct.,  what  do  the  two  together  cost? 
What  change  should  be  received  from  a  $5  bill 
paid  the  grocer? 

8.  A  woman  buys  3  boxes  of  soda  crackers  at 
9  ct.  a  box,  and  4  boxes  of  oatmeal  crackers  at 
12  ct.  a  box.     She  hands  the   grocer  a   $1  bill. 
How  much  change  is  due  her? 

9.  John's   mother  sent   him  to  buy  some   gro- 
ceries.    He  paid  33  ct.  for  chocolate,  35  ct.  for 
coffee,  48  ct.   for  tea,  and  bought  ^  Ib.   of  wal- 
nuts at  18  ct.  a  pound.    He  gave  the  grocer  $1.50. 
How  much  change  was  due  him? 


280  PRIMARY   ARITHMETIC 

10.  A  farmer  paid  $210  for  sheep  at  $6  each. 
How  many  did  he  buy? 

11.  A  dealer  bought  9  tables  for  $135.     How 
much  did  each  table  cost? 

12.  A   farmer    bought    32    sheep    at    $7    each. 
How  much  did  they  cost? 

13.  A  man  saved  $27  a  month  for  8  months. 
How  much  did  he  save  in  all? 

14.  In  a  certain  city  the  length  of  3  blocks  is 
792  ft.     What  is  the  average  length  of  a  block? 

15.  There   are    280   children   in  a  school   of    8 
grades.     How  many  are  there,  on  an  average,  in 
each  grade? 

16.  Which  amounts  to  more,  $48  a  month  for 
2  months,  or  $34  a  month  for  3  months?    How 
much  more? 

17.  In  a  certain  school  they  use  252  pencils  a 
term.     Allowing  2  pencils  to  each  pupil,  how  many 
pupils  are  there  ? 

18.  Some  bricks  are  piled  one  on  top  of   the 
other  to  a  height  of  78  in.     The  bricks  are  2  in. 
thick.     How  many  are  there? 

19.  A   man    saved  '$224   in   7  months.      How 
much  did  he  save,  on  an   average,  each  month? 
How  much  did  he  save  in  6  months? 

20.  A  man  saved  $16.75  in  January,  $14.60  in 
February,  and   $21.85  in  March.      In  April  his 
expenses  required  him  to  use  $6.75  of  his  savings. 
How  much  had  he  left  ? 


REVIEW  281 

BEVIEWING  PAGES  129-170 
ORAL   EXERCISE 

1.  What  do  4000  pounds  of  coal  cost  at  $5.50 
a  ton? 

2.  Which  is  the  greater,  £  of  93  or  £  of  120? 
How  much  greater? 

3.  How  many  square  yards  of  cloth  in  a  piece 
6  yd.  long  and  2  yd.  wide? 

4.  How  many  square  yards   in  a   playground 
120  ft.  long  and  30  ft.  wide? 

5.  How   many    days    are    there    in    February, 
March,  and  April,  1907?    1908? 

6.  How  many  days  are  there  beginning  with 
September  1  and  ending  with  October  30? 

7.  If  you  leave  home  at  half  past  8,  and  return 
at  a  quarter  past  12,  how  long  are  you  away? 

8.  A  schoolroom  has  3  windows,  each  contain- 
ing 12  sq.  ft.     How  many  square  yards  in  all? 

9.  School  opens  at  9  and  closes  at  4.     Allowing 
an  hour  and  a  half  for  intermissions,  how  long  are 
we  at  work  in  school  in  a  day? 

10.  John  and  Henry  were  born  the  same  year, 
John  on  January  21  and  Henry  on  February  28. 
John  is  how  many  days  older  than  Henry  ? 

11.  A  40-ft.  telegraph  pole  lies  across  the  street 
at  right  angles  to  the  walks.     It  is  10  ft.  from  one 
sidewalk  and  6  ft.  from  the  opposite  one.     The 
sidewalks  are  5  ft.  wide.     How  wide  is  the  street? 


282  PRIMARY    ARITHMETIC 

WRITTEN   EXERCISE 

1.  A  dealer  pays  $2112  for  22  horses.     What 
is  the  average  price? 

2.  If  a  man  works  23  days  at  $1.75  a  day,  how 
much  does  he  receive? 

3.  How   far  is  it  around  a  city  block  that  is 
392  ft  long  and  276  ft.  wide? 

4.  How  many  bushels  of  corn  at  42  ct.  a  bushel 
can  be  bought  for  7350  ct.,  or  $73.50? 

5.  A  man  saves  on  an  average  $227.85  a  year 
for  8  years.    How  much  does  he  save  in  all? 

6.  How  many  more  head  of  cattle  can  be  bought 
for  $672  at  $32  a  head  than  at  $42  a  head? 

7.  What  would  the  food  cost  during  July  for 
an  army  of  25,000  soldiers,  allowing  39  ct.  a  day 
for  each  soldier? 

8.  On  a  lot  which  cost  $650  there  is  built  a 
house  costing  $2835.50  and  a  barn  costing  $286.50. 
What  is  the  total  cost? 

9.  There  are  375  pupils  in  the  Lincoln  School, 
523  in  the  Lee  School,  and  in  the  Jefferson  School 
there  are  half  as  many  as  in  the  other  two  together. 
How  many  are  there  in  the  three? 

10.  Some  workmen  in  a  railway  camp  ate  in  one 
day  40  Ib.  of  bacon  at  18  ct.  a  pound,  65  loaves 
of  bread  at  4  ct.  a  loaf,  2  bu.  of  potatoes  at  45  ct. 
a  bushel,  and  butter,  coffee,  and  milk  amounting 
to  $6.75.  What  did  the  day's  food  cost? 


REVIEW  283 

EEVIEWING  PAGES  171-212 

WRITTEN    EXERCISE 

1.  Mr.  Richards  pays  $12  a  month  rent  for  6J 
years.     How  much  does  he  pay  in  all? 

2.  How  many  bushels  of  corn  at  45  ct.  a  bushel 
will  pay  for  115  tons  of  coal  at  $5.22  a  ton? 

3.  A  carload  of  potatoes  containing  316  bu.  was 
sold  for  $145.36.     How  much  was  that  a  bushel? 

4.  If  a  gasolene  stove   uses  2  qt.  of  gasolene 
daily,  at  a  cost  of  15  ct.  a  gallon,  wrhat  is  the  cost 
of  running  it  during  April? 

5.  Ruth's  clothes  for  one  year  cost  $12.40,  Mary's 
cost  half  as  much,  and  John's  cost  $2  more  than 
Mary's.     What  did  they  all  cost? 

6.  There    are    416    pupils    in    the   Washington 
School.     The  annual  cost  of  running  it -is  $6240. 
What  is  the  average  cost  for  each  pupil? 

7.  A  factory  paid  out  $99,360  in  wages  in  360 
days.     If  the  average  amount  paid  to  each  work- 
man was  $3,  how  many  workmen  were  there? 

8.  A  man  bought  48  yd.  of  carpet  at  $1.25  a  yard, 
18|  double  rolls  of  paper  at  64  ct.  a  single  roll,  4 
chairs  at  $2.16  each,  and  a  sofa  costing  $11.75. 
What  was  the  total  cost? 

9.  Two  automobiles  are  216  mi.  apart.     If  they 
travel  towards  each  other,  one  at  the  rate  of  17  mi. 
an  hour  and  the  other  7  mi.  an  hour  slower,  how 
long  before  they  will  meet? 


284  PRIMARY  ARITHMETIC 

ORAL  EXERCISE 

1.  State  1  of  8;    16;    24;   30;   40;    80;    5;   7. 

2.  State^  of  9;  ]5;  21;  18;  30;  60;  5;  7;  11. 

3.  State  §  of  3;  6;  9;  12;  21;  18;  30;  60;  90. 

4.  State  \  of  8;  16;  24;  32;  40;   44;   80;  5. 

5.  State  f  of  12;  8;  20;   16;  24;  32;   40;  44. 

6.  State^  of  10;  20;  5;   15;  30;  25;  50;  55. 

7.  State  l  of  12;  24;  30;  18;  42;  36;  60;  66. 

Add  the  following: 

8-   i  I ,  i,  i,  I-  9-  1,  I,  i  f ,  |,  f 

10.  If,  2i,  3|,  5f .  11.  2*,  3f,  6|,  6|,  7. 

Subtract  as  indicated: 

12.   f-i.      13.  f-l.       14.   |-|.      15.  |__V 

16.  f-1       17.  f-^.     18.   |-l.      19.  l|-f. 

WRITTEN  EXERCISE 

1.  How  many  cubic  feet  in  a  car  32  ft.  by  8  ft. 
by  6ft.? 

2.  How  many  cords  of  wood  will  the  car  hold? 

3.  A  car  load  of  coal  containing  33,000  Ib.  is 
sold  at  $5.50  a  ton.     What  is  the  cost? 

4.  How  many  tiles  6  in.  square  will  be  required 
for  a  hall  floor  27  ft.  long  and  9  ft.  wide? 

5.  Represent  on  a  scale  of  2  ft.  to  the  inch  a 
rectangle  18  ft.  by  12  ft.     Find  the  area. 

6.  What  is  the  cost  of  a  pile  of  wood  120  ft. 
long,  4  ft.  wide,  and  4  ft.  high,  at  $4.75  a  cord? 


KEVIEW  285 

EEVIEWING  PAGES  213-257 

ORAL  EXERCISE 


Study  pages  157  and  %%7,  and  then  tell  the  cost 
of  the  following  : 

1.  160  books  at  50  ct.;  at  25  ct. 

2.  40  primers  at  20  ct.;  at  25  ct. 

3.  150  knives  at  331  ct.;  at  50  ct. 

4.  24  Ib.  of  tea  at  50  ct.;  at  33|  ct. 

5.  105  gal.  of  oil  at  20  ct.;  at  10  ct. 

6.  32  Ib.  of  coffee  at  25  ct.;  at  50  ct. 

7.  18  Ib.  of  meat  at  16|  ct.;  at  20  ct. 

8.  444  yd.  of  cloth  at  25  ct.  ;  at  50  ct. 

9.  60  Ib.  of  cheese  at  16f  ct.;  at  20  ct. 

10.  24  Ib.  of  meat  at  121  ct.  ;  at  16f  ct. 

11.  306  yd.  of  cloth  at  33J  ct.;  at  50  ct. 

12.  120  Ib.  of  butter  at  331  ct.  ;  at  25  ct. 

13.  160  qt.  of  berries  at  121  ct.;  at  10  ct. 

WRITTEN  EXERCISE 

Write  the  eost,  without  multiplying  in  full: 

1.  12  yd.  of  cloth  at  25  ct.  ;  at  331  ct. 

2.  408  yd.  of  cloth  at  25  ct.;  at  50  ct. 

3.  2  doz.  coats  at  $25  each;  at  $20  each. 

4.  4  umbrellas  at  $2.50  each;  at  $2.25  each. 

5.  12i-3|.  6.  4f-lf.  7.  21-11 

8.  21f  +  16|+102i  +  27i  +  5f. 

9.  2i 


286  PRIMARY    ARITHMETIC 

WRITTEN   EXERCISE 

Write  as  decimal  fractions : 

1.  f       2.  f       3.   TV       4.   TV       5.  ^.       6.  l. 
7.  7  tenths.  8.  25  hundredths. 

9.   7  hundredths.  10.  25  tenths  (=  2.5). 

11.  375  hundredths.          12.   37  tenths  ;  8  tenths. 

13.  Forty-two,  and  forty-two  hundredths. 

14.  3,  and  75  hundredths  ;  99  hundredths. 

15.  300,  and  75  hundredths;  5  hundredths. 

16.  Three  hundred  seventy-five  thousandths. 

17.  45  tenths;   75  tenths;   8 1- tenths;  5^  tenths. 

18.  Three  hundred,  and  seventy-five  thousandths. 

19.  Six,  and  five  tenths ;  sixty-five  tenths ;  six 
and  a  half ;  thirteen  halves. 

20.  Five  hundred  fifteen  thousandths ;  five  hun- 
dred, and  fifteen  thousandths. 

21.  Of  8320  bu.  of  com  .15  is  damaged.     How 
many  bushels  are  not  damaged? 

22.  A  certain  room  is  31.8  ft.  long  and  22.04  ft. 
wide.     How  far  is  it  around  the  room? 

23.  If  the  average  cost  per  mile  of  a  certain 
railroad  is  $10,850,  what  is  the  cost  of  .15  mi.? 

24.  A  cubic  foot  of  water  weighs  62^  lb.,  and  a 
gallon  of  water  weighs  8.33  lb.     What  is  the  dif- 
ference in  weight? 

25.  It  is  270.02  mi.  from  Chicago  to  Cedar  Rapids, 
and  220.8  mi.  from  Cedar  Rapids  to  Omaha.    How 
far  is  it  from  Chicago  to  Omaha? 


REVIEW  287 

Multiply  as  folloivs: 

26.  25  by  .6.  27.  37  by  .9.  28.  48  by  .7. 

29.  275  by  .8.  30.  327  by  .6.  31.  432  by  .5. 

32.  23  by  .23.  33.  38  by  .42.  34.  26  by  .81. 

35.  134  by  .72.  36.  243  by  .86.  37.  355  by  .74. 

38.  285  by  .48.  39.  496  by  .39.  40.  327  by  .77. 

41.  829  by  .34.  42.  642  by  .73.  43.  929  by  .29. 

Find  the  cost  of  each  of  the  following : 

44.  2|  Ib.  tea  @  44/.  45.  li  Ib.  cocoa  @  58/. 
46.  3f  Ib.  figs  @  24/.  47.  7f  Ib.  prunes  @  8/. 
48.  3f  Ib.  steak  @  16/.  49.  27 j  yd. calico  @12X. 

50.  21  Ib.  chocolate  @  36/. 

51.  3|  Ib.  crackers  @  22X. 

52.  3  Ib.  8  oz.  cereal  @  8X. 

53.  25i-lb.  bag  of  flour  @  4X. 

54.  \  is  what  part  of  {?  of  |?  of  1  ?  of  2?  of  5? 

55.  TL  is  what  part  of  |?  of  i?  of  2l?  of  1  ?  of  2? 

56.  i  is  what  part  of  1?  of  1?  of  2?  of  5?  of  10 ? 

57.  How  much  is  £  of  £?  J  of  1?  |  of  }?  TV  of  1? 

58.  Express^ as  20ths;  Jasl2ths;  y1^ as  lOOths. 

59.  Reduce  to  lowest  terms:  |$,  T\,  ^j,  2-8j,  -j6,-. 

60.  Multiply  $5.75  by  120;  by  300;  by   275. 

61.  Add  16  ft.  8  in.,  21  ft.  9  in.,  3  ft.  7  in.,  4  ft. 
11  in.,  5  ft.  10  in. 

62.  How  many  cords  of  wood  in  a  pile  96  ft.  long, 
6  ft.  high,  4  ft.  wide? 

63.  How  many  square  inches  in  a  rectangle  3  yd. 
2  in.  long,  and  21  ft.  wide? 


288  PRIMARY   ARITHMETIC 

ORAL  EXERCISE 

State  the  cost  of  the  following : 

1.  4  hats  @  $1.50.  2.  8  books  @  $1.50. 

3.  8  lamps  @  $1.25.         4.  40  sleds  @  $1.10. 

5.  150  dolls  @  33JX.         6.  12  vases  @  $1.25. 

7.  20  books  @  $1.05.       8.  35  jackets  @  $1.20. 

9.  25  books  @  $1.20.  10.  12  chairs  @  $1.33£. 

11.  9  frames  @  $1.33$.  12.  30  pictures  @  $1.05. 

13.  30  baskets  @  $1.10.  14.  600  Ib.  butter  @  33JX. 

15.  400  doz.  eggs®  12  |X.  16.  800  qt.  berries®  12  JX. 

WRITTEN  EXERCISE 

J^'nrf  £^e  cos£  o/"  the  following : 
1.  272  chairs  @  $1.50.     2.  478  books  @  $1.50. 
3.  364  rugs  @  $1.25.     4.  154  lamps  @  $1.25. 
5.  123books@$1.33f    6.  108  vases  @  $1.33. 
7.  115  chairs  @  $1.20.     8.  205  clocks  @  $1.20. 
9.  152doz.eggs@12i/.  10.  116  Ib.  butter  @  25X. 

Make  out  Nils  for  the  following,  as  on  page  237: 

11.  3  Ib.  sugar  @  6JX,  3  gal.  oil  @  17X. 

12.  2|  doz.  oranges  @  48X,  i  doz.  bananas  @  24X. 

13.  25  arithmetics  @  SOX,  8  doz.  tablets  @  36X, 
2  doz.  bottles  ink  @  94X. 

14.  121  yd.  calico  @  14X,  |  yd.  velvet  @  $1.60, 
18  yd.  embroidery  @  12^X. 

15.  If  1  cu.  ft.  of  water  weighs  62.5  Ib.,  what  is 
the  weight  of  the  water  in  a  tank  6  ft.  6  in.  long, 
5  ft.  wide,  and  4  ft.  deep? 


ANSWERS 


Answers  are  given  to  the  Written  Exercises  only,  begin- 
ning on  page  39. 

Page  39 


1. 

55. 

2 

.  92. 

3. 

89. 

4. 

79. 

5. 

88. 

6. 

77. 

7 

.  68. 

8. 

89. 

9. 

99. 

10. 

98. 

11. 

68. 

12 

.  58. 

13. 

78. 

14. 

79. 

15. 

88. 

16. 

89. 

17 

.  77. 

18. 

76. 

19. 

78. 

20. 

98. 

21. 

88. 

22 

.  78. 

23. 

98. 

24. 

88. 

25. 

39. 

26. 

36. 

27 

.  78. 

28. 

39. 

29. 

46. 

30. 

47. 

31. 

77. 

32 

.  69. 

33. 

58. 

34. 

23. 

35. 

19. 

36. 

16. 

37 

.  19. 

38. 

22. 

39. 

18. 

40. 

15. 

41. 

16. 

42 

.  15. 

43. 

30. 

44. 

76. 

Page  40 

1. 

36. 

2.  48 

ct. 

3. 

48. 

4. 

10  ct. 

5. 

6  qt. 

6.  21 

ft. 

7. 

49  Ib. 

8. 

$15. 

9. 

77  Ib. 

10.  17, 

11. 

21. 

12. 

$38. 

13. 

$65. 

14.  $6 

8. 

15. 

38  boys. 

16. 

37  girls. 

17. 

47. 

18.  87 

19. 

89. 

20. 

108. 

21. 

77. 

22.  98 

23. 

49. 

Page  41 

1. 

25. 

2.  43. 

3.  62. 

4.  40. 

5.  34. 

6. 

11. 

7. 

32. 

8.  41. 

9.  13. 

10.  41.      11.  20. 

12. 

11. 

Page  42 

1.  16.  2.  37.  3.  75.  4.  57  ct. 

1 


ANSWERS 


Page 

43 

1. 

22. 

2. 

12. 

3. 

21. 

4. 

16. 

5 

.  41. 

6. 

81. 

7. 

31. 

8. 

16. 

9. 

11. 

10 

.  35. 

11. 

61. 

12. 

71. 

13. 

43. 

14. 

61. 

15 

.  16. 

16. 

10. 

17. 

60. 

18. 

10. 

19. 

10. 

20 

.  12. 

21. 

10. 

22. 

12. 

23. 

80. 

24. 

33. 

25 

.  30. 

26. 

11. 

27. 

20. 

28. 

20. 

29. 

40. 

30 

.  12. 

31. 

21. 

32. 

30. 

33. 

25. 

34. 

17. 

35 

.  46. 

36. 

16. 

37. 

66. 

38. 

70. 

39. 

71. 

40 

.  14. 

41. 

20. 

42. 

10. 

43. 

30. 

44. 

11. 

45 

.  33. 

46. 

42. 

47. 

33. 

48. 

81. 

49. 

52. 

50 

.  22. 

51. 

15. 

52. 

62. 

53. 

66. 

54. 

48. 

55 

.  71. 

56. 

31. 

57. 

51. 

58. 

62. 

59. 

30. 

60 

.  1. 

61. 

40. 

62. 

1. 

63. 

61. 

64. 

34. 

65 

.  20. 

66. 

40. 

67. 

24,  18. 

68. 

66. 

69. 

33. 

70 

.  71. 

Page 

44 

1. 

41  ct. 

2. 

6. 

3 

.  21 

4 

.  31. 

5. 

16. 

6. 

60. 

7. 

70. 

8 

.  44 

9 

.  53. 

10. 

21ft 

11. 

70  ct. 

12. 

62. 

13 

.  50 

ct. 

14 

.  62 

ft. 

15.  52. 

16. 

3yd. 

17. 

70yd. 

18 

.  42 

19 

.  3. 

20.  6. 

21. 

14. 

22. 

37. 

23 

.  60 

24 

.  42. 

25. 

60. 

26. 

73. 

27. 

58. 

28 

.  61 

29 

.  26. 

30. 

11. 

31. 

2. 

32. 

3. 

33 

.  4. 

34 

.  13. 

35. 

30. 

36. 

40. 

37. 

53. 

38 

.  23 

39 

.  33. 

40.  75. 

41. 

53. 

42. 

55. 

43 

.  38 

44 

.'47. 

45.  39- 

46. 

80. 

47. 

76. 

48 

.  71 

49 

.  21. 

50. 

1. 

51. 

21. 

52. 

62. 

53 

.  81 

54 

.  51. 

Page  47 

1.  3,  30,  2,  20,  1,  10,  4,  40,  2,  20,  1,  10. 

2.  95  ct.,  69  lb.,  78  qt.,  $78. 


ANSWERS 

Page  54 
1.  958,  886,  644,  788.  2.  452,  472,  282,  513. 

Page  55 

1.  32  ft.,  333  ft.,  9  in.,  33  ft.,  337  ft. 

2.  29  ft.,  229  ft.,  3  in.,  25  ft.,  225  ft. 

Page  56 

1.  91b.,  90  lb.,  900  lb.,  935  Ib. 

2.  5  lb.,  50  lb.,  500  lb.,  512  lb. 

Page  57 
1.  46  lb.  10  oz.  2.  85  lb.  12  oz. 


Page 

58 

1.  676. 

2.  888. 

3.*  799. 

4.  695. 

5.  869. 

6.  787. 

7.  788. 

8.  558. 

9.  888. 

10.  797. 

11.  487. 

12.  798. 

13.  888. 

14.  678. 

15.  648. 

16.  $466. 

17.  378  in. 

18.  758  ft. 

19.  1099  ft. 

20.  $386. 

21.  377  lb. 

22.  388  lb. 

23.  296  yd. 

24.  $444. 

25.  $888. 

26.  617yd. 

27.  $777. 

28.  $566. 

Page 

59 

1.  305. 

2.  411. 

3.  223. 

4.  514. 

5.  635. 

6.  414. 

7.  355. 

8.  453. 

9.  227. 

10.  651. 

11.  871. 

12.  922. 

13.  822. 

14.  75. 

15.  573. 

16.  139. 

17.  331. 

18.  $477. 

19.  $252. 

20.  $355. 

21.  $376. 

22.  $475. 

23.  $756. 

24.  $500. 

25.  $650. 

26.  $820. 

27.  $233. 

28.  188ft. 

29.  496ft. 

30.  166  yd. 

31.  139  in. 

32.  105. 

33.  102. 

34.  22.         35.  11 

36.  110 

37.  110. 

i  ANSWERS 

Page  61 
1.  10  pt.,  5  qt.          2.  8  qt.,  2  gaL  3.  10  bu.,  10  gal. 

Page  63 
1.  7  da.,  1  wk.  .      2.  60  sec.,  1  min.        3.  60  sec.,  1  min. 

Page  64 
1.  6  sq.  in.,  10  sq.  ft.,  30  sq.  in.,  25  sq.  ft. 

Page  79 


1.  65 

2.  75. 

3.  87. 

4.  74. 

5.  80. 

6.  81. 

7.  92. 

8.  76. 

9.  83. 

10.  83. 

11.  128. 

12.  189. 

13.  239. 

14.  147. 

15.  206. 

16.  175. 

17.  178. 

18.  188. 

19.  148. 

20.  129. 

Page  80 

1.  80.  2.  91.  3.  68.  4.  63.  5.  77. 

6.  383.  7.  767.  8.  760.  9.  831.         10.  960. 

Page  81 

1.  469.         2.  473.         3.  503.         4.  613.         5.  712ft. 
6.  671.         7.  861.         8.  $922. 

Page  82 


1. 

836. 

2. 

868. 

3. 

832. 

4. 

909. 

5. 

725. 

6. 

464. 

7. 

927. 

8. 

437. 

9. 

910. 

10. 

418. 

11. 

696. 

12. 

770. 

13. 

500. 

14. 

888. 

15. 

600. 

16. 

$300. 

17. 

$900. 

18. 

$650. 

19. 

$700. 

20. 

440  ft. 

21. 

761  ft. 

22. 

500  yd. 

23. 

404  yd. 

24. 

154  Ib. 

25. 

245  Ib. 

26. 

247  Ib. 

ANSWERS 
Page  83 


1. 

958. 

2. 

957. 

3. 

745. 

4. 

955. 

5. 

836. 

6. 

208. 

7. 

199. 

8. 

228. 

9. 

226. 

10. 

219. 

11. 

238. 

12. 

469. 

13. 

626. 

14. 

531. 

15. 

710. 

16. 

690. 

17. 

905. 

18. 

704. 

19. 

504. 

20. 

805. 

21. 

339. 

22. 

759. 

23. 

667. 

24. 

646. 

25. 

325. 

26. 

528. 

27. 

$783. 

28. 

$665. 

29. 

$867. 

30. 

165  in. 

31.  129 qt.  32.  373ft.    33.  423ft.   34.  629ft.  35.  101yd. 


Page  85 

1.  109.       2.  202.       3.  $137.       4.  295ft.       5.  189  min. 
6.  192.     7.  280.     8.  174.      9.  694.     10.  215.     11.  211. 


Page  86 


1. 

217. 

2. 

264. 

3. 

396. 

4. 

598. 

5. 

280. 

6. 

789. 

7. 

306. 

8. 

19. 

9. 

198. 

10. 

494. 

11. 

399. 

12. 

109. 

13. 

299. 

14. 

79. 

15. 

352. 

16. 

494. 

17. 

188. 

18. 

496. 

19. 

84. 

20. 

81. 

21. 

165. 

22. 

$136. 

23. 

$250. 

24. 

$575. 

25. 

233  ft. 

26. 

155  ft. 

27, 

255  yd. 

28. 

187yd. 

29. 

268  min. 

30. 

52ft. 

31. 

781  ft. 

32. 

605. 

33. 

745. 

34. 

570. 

35. 

199. 

36. 

708. 

37.  558.  38.  578.              39.  289.             40.  345. 

41.  448.  42.  $557.           43.  $167.           44.  428. 

45.  619.  46.  143.        47.  249.        48.  563.        49.  215. 

Page  87 

1.  69.  2.  92.               3.  50.            4.  75.            5.  90. 

6.  51.  7.  39.               8.   114.          9.   57.           10.  54. 

11.  84.  12.  111.       13.  92.      14.  72.      15.  48.     16.  56. 


ANSWERS 


Page  88 

1. 

52. 

2. 

74. 

3. 

96. 

4.  78. 

5. 

94. 

6. 

45. 

7. 

72. 

8. 

78. 

9.  87. 

10. 

84. 

11. 

68. 

12. 

76. 

13. 

100. 

14.  132. 

15. 

144. 

16. 

75. 

17. 

85. 

18. 

130. 

19.  160. 

20. 

185. 

21. 

135. 

22. 

156. 

23. 

272. 

24.  292. 

25. 

410. 

26. 

182. 

27. 

178. 

28. 

279. 

29.  380. 

30. 

480. 

31. 

70. 

32. 

90  ct. 

33. 

132. 

34.  132. 

35. 

310. 

36. 

$150. 

37. 

$165. 

38. 

$128. 

39.  355ft. 

40. 

100  ct. 

41.  164  Ib. 

42 

.  99yd. 

Page  89 

1. 

$34. 

2.  $9 

6. 

3. 

$42. 

4. 

150  ct. 

Page  90 

1. 

21. 

2. 

12. 

3. 

11. 

4.  34. 

5.  32. 

6. 

11. 

7. 

124. 

8. 

232. 

9.  211. 

10.  112. 

11. 

110. 

12. 

101. 

13. 

213. 

14.  103. 

15.  322. 

16. 

313. 

17. 

231. 

18.  112. 

19. 

200. 

20. 

100. 

21.  4,40. 

Page  92 
1.  180  min.  2.  90  min. 

Page  93 

1.  XX,  XII,  VII,  VI,  XVIII,  XVI,  XIX,  XV. 

2.  11,  9,  4,  6,  19,  14,  17. 

Page  94 

1.  2345,  7890,  6789. 

2.  Two  thousand  one  hundred  forty-three  ;  nine  thousand 
nine ;  nine  thousand  eight  hundred  seventy-six. 


ANSWERS  7 

Page  95 

1.  IV,    XLII,    LXXIII,    LXXV,    LXXIX,    LXXXIV, 
LXXXIX. 

2.  39,  44,  79,  88.      . 

Page  96 

$1.05,  $7.16,  $925.25,  $17.50. 

Page  97 

1.  4.  2.   $1,  $4. 

Page  98 

1.  $3.20  2.  $7.30.  3.  $8.  4.  $6.13. 

Page  99 
1.  180°.  2.  66°.  3.  16°.  4.  47°. 

Page  100 
1.  38  ft.  3.  2J-  in. 

Page  101 
1.  16  sq.  in.      2.  4  sq.  ft.      3.  6  sq.  yd.      4.  3  in.,  9  sq.  in. 

Page  102 
1.  270  sq.  yd.  2.  270  sq.  ft.  3.  170  sq.  yd. 

Page  105 

1.  45  cu.  in.        2.  88  cu.  ft.        3.  96  cu.  ft. 
4.  90  cu.  in.,  126  sq.  in.    5.  96  cu.  in.,  124  sq.  in. 

Page  106 
1.  f,  §.  2.  12,  6,  20,  15. 

Page  108 

1.  284.    2.  220.    3.  528.   4.  1012.    5.  570. 
6.  5857.   7.  5795.   8.  2112.   9.  $8.85.   10.  $10.11. 


ANSWERS 


1.  4428. 
6.  2359. 

Page  109 

2.  4412.   3.  4172.  4.  $37.72. 
7.  2623.   8.  3318.  9.  $82.68. 

5.  $31.21. 
10.  $43.92. 

Page  110 

1.  2829. 

2.  5403. 

3.  7062. 

4.  7636. 

5.  5979. 

6.  7103. 

7.  7661. 

8.  7631. 

9.  8993. 

10.  6877. 

11.  7920  ft. 

12.  $7125. 

13.  9240  ft. 

14.  $4575. 

15.  $4860. 

16.  $5920. 

17.  6129. 

18.  5469. 

19.  6878. 

20.  $725. 

21.  $515. 

22.  $442. 

23.  $748. 

24.  $363. 

25.  $275. 

26.  1888. 

27.  1079. 

28.  1572. 

29.  1188. 

30.  805. 

31.  358. 

32.  1627. 

33.  975. 

34.  761. 

35.  1838. 

36.  1005. 

370  989. 

38.  3485. 

39.  82. 

40.  1067. 

41.  4250. 

42.  404. 

43.  2581. 

44.  5009. 

45.  223. 

46.  2192. 

Page  111 

1.  34. 

2.  43.     3. 

32.     4.  22. 

5.  13. 

6.  21. 

7.  12.     8. 

20.     9.  21. 

10.  11. 

11.  100. 

12.  110.    13. 

122.   14.  124. 

15.  433. 

16.  201. 

17.  303.    18. 

202.   19.  198. 

20.  192. 

21.  385. 

22.  1039.   23. 

1096.  24.  396. 

25.  1711. 

26.  1089. 

27.  3497.   28. 

109.   29.  2047. 

30.  5928. 

31.  1825. 

32.  991.   33. 

4052.  34.  2707. 

35.  6901. 

36.  $3060.  37.  $7913.   38.  $8.51.  39.   $7.63.  40.  $4.94. 

41.  $6.74.    42.  $6.11.    43.  $6.17.  44.  9216.     45.  2969. 

46.  2631.      47.  4272.      48.  2676.     49.  1451.     50.  3115. 

51.  6427.  52.  3850. 

Page  113 

2.  240,  246,  306,  420,  486.      3.  $6,  7  ft,  9  ct.,  8  yd. 


ANSWERS 


Page  114 

1. 

36. 

2. 

20. 

3. 

22. 

4 

.  25. 

5. 

22. 

6. 

32. 

7. 

30. 

8. 

30. 

9 

.  20. 

10. 

39. 

11. 

44. 

12. 

54. 

13. 

24. 

14 

.  29. 

15. 

34. 

16. 

52. 

17. 

36. 

18. 

39. 

19 

.  78. 

20. 

30. 

21. 

49. 

22. 

37. 

23. 

60. 

24 

.  85. 

25. 

53  ct. 

26. 

30. 

27. 

27. 

Page  115 

2.  210,  427,  301,  175,  168,  245,  644,  469,  343. 

3.  9,  6,  $8,  4  ft.,  7  in.,  10  yd.    .  4.  30. 

Page  117 

2.  270,  333,  603,  243,  414,  441. 

3.  $9,  10  ft.,  7  in.,  6  bu.  4.  5  yd. 

Page  121 


1.  315. 
6.  704. 

2.  432.    3.  609.    4.  576. 
7.  765.    8.  441.    9.  630. 
11.  2849.       12.  6616. 

5.  686. 
10.  1722. 

Page  122 

1.  81b. 

2.  $: 

L.84. 

Page  123 

1.  55. 

2.  75. 

3.  137. 

4. 

81. 

5.  92. 

6.  124. 

7.  132. 

8.  119. 

9. 

122. 

10.  102. 

11.  93. 

12.  79. 

13.  370. 

14. 

470. 

15.  991. 

16.  1426. 

17.  256. 

18. 

1147. 

Page  125 

1.  811. 

2.  822. 

3. 

872. 

4.  1287. 

5.  137. 

6.  1401.       7. 

$125. 

8.  28. 

10  ANSWERS 

Page  126 

1.  30.  2.  1800,  21,600. 

3.  730  gal.  4.  40  ct.,  $2.80,  $11.20. 

Page  127 
1.  $2091.50.         2.  $117.45.        3.  $3900.        4.  $87.20. 

Page  128 

1.  $5426.73.     2.  $6727.65.  3.  $2431.10.     4.  $1940.32. 

5.  $8491.60.     6.  $7818.47.  7.  794.  8.  1906. 

9.  99.  10.  1516.  11.  $37.18.  12.  $38.87. 

13.  $39.09.  14.  $364.39.  15.  $2982.  16.  $2943. 

17.  $2315.  18.  $2120.  19.2538ft.  20.2512yd. 

21.  716.  22.  623.  23.  858.  24.  1233. 
25.  1370'.                        26.  1787J. 

Page  130 

1.  DLXII,  DCCXLIII,  DCCCXXVII,  CCCXXIX,  CI. 

2.  323,  459,  777,  401,  808. 

Page  131 
1.  $16.93.         2.  $62.45.         3.  $605.25. 

Page  132 

1.  $16.11.    2.  $17.10.   3.  $172.25.    4.  $110.11. 
5.  $287.95.   6.  $81.77.   7.  $1053.25.   8.  $1311.20. 

Page  133 

1.  $17.85.          2.  $18.50.         •  3.  $69.60. 

4.  $128.25.         5.  $225.  6.  $438. 

Page  134 

1.  $47.49.     2.  $16.87.     3.  $17.78.    4.  $4.89. 

5.  $29.92.     6.  545.       7.  6489.     8.  2892. 


ANSWERS  11 

9  92.  10.  7849.  11.  1340ft.  12.  873yd. 

13  5959  Ib.  14.  1877  gal.  15.  $889.  16.8541. 

17  2413.  18.  3939.  19.  969.  20.  1764. 

21  $3.88.  22.  $34.25.  23.  $53.73.  24.  $23.22. 

Page  136 

1.  $11.25.         2.  $9.  3.  $14.25.          4.  $89.52. 

5.  $9640.          6.  $80.37.          7.  $21.14.          8.  $187.68. 
9.  $96.40.       10.  $73.50.        11.  $5.81. 

Page  137 

1.  $3.  2.  $3.50.  3.  $2.40.  4.  60  ct. 

5.  270,  270,  540.  6.  $3.50,  70  ct.,  $4.20. 

Page  139 

1.  1651.  2.  8442.  3.  11,200.  4.  8820. 

5.  13,314.  6.  10,191.  7.  8890.  8.  5742.  - 
9.  7562.            10.  8643.            11.  $7425.            12.  $216. 

Page  140 

1.  $72.30.  2.  $71.94.  3.  $77.71.  4.  $83.16.     5.  $106.78. 

6.  $54.21.  7.  $80.73.  8.  $59.50.  9.  $49.68.   10.  $24. 

11.  $48,  $18,  $66.       12.  $12,  $48.       13.  $98. 

Page  141 
1.  7800  sq.ft.  2.  7800  cu.  ft.  3.  558  Ib.  4.  1950  cu.  ft. 

Page  142 

1.  $81.     2.  189.     3.  $788.     4.  $972. 

5.  690.     6.  429.     7.  71  bbl.    8.  $800,  $5600. 


12  ANSWERS 

Page  143 


1.  $2.16. 

2. 

$4.32. 

3. 

$9.31. 

4.  $2.05. 

5.  $4.16. 

6. 

$6.05. 

7. 

$36.25. 

8.  $2.20. 

9.  $1.44. 

10.  $27.50,  $275. 

11.  $4.50, 

$22.50. 

Page  144 

1.  21, 

2. 

2. 

3.  350. 

4.  6. 

5.  15. 

6.  320. 

7. 

37. 

8.  19. 

9.  91. 

10.  37. 

11.  15. 

12. 

$123. 

13.  46. 

14.  59. 

15.  38. 

Page  145 

1.  270. 

2. 

3024. 

3.  42. 

4.  231. 

5.  24. 

Page  146 

1.  21. 

2. 

51. 

3.  71. 

4.  112. 

5.  342. 

6.  876. 

7. 

486. 

8.  546. 

9.  647. 

Page  147 

1.  235. 

2. 

126. 

3.  347. 

4.  158. 

5.  119. 

6.  218. 

7. 

125. 

8.  118. 

9.  119. 

10.  99. 

11.  111. 

12. 

123. 

13.  89. 

14.  111. 

15.  117. 

16.  35. 

17. 

19. 

18.  21. 

Page  148 

1.  403. 

2. 

503. 

3.  402. 

4.  102. 

5.  532. 

6.  111. 

7. 

120. 

8.  51. 

9.  102. 

Page  149 

1.  213. 

2. 

350. 

3.  240. 

4.  210. 

5.  130. 

6.  111. 

7. 

180. 

8.  73. 

9.  92. 

ANSWERS  13 

Page  151 

1.  $1.82.  2.  45  ct.  3.  $1.35.  4.  $1.88. 

Page  153 

2.  1  yd.        3.  30  ct.       4.  15  in.       5.  lj  yd.       6.  25  ct. 

Page  155 

1.  243,  486.  2.  209,  418,  627. 

3.  47,  94,  141,  188.  4.  122,  244,  366,  488. 

5.  18  mi.,  12  mi. 

Page  156 

4.  1278,  672J,  249|,  314|. 

Page  157 

1.  55  ct.  2.  95  ct. 

3.  $1.11§,  $1.50,  $1.70,  $0.95. 

4.  $0.50,  $0.20,  $0.80,  $387.88. 

Page  158 

1.  4  oz.,  8  oz.  2.  Jib.,  fib.,  lib.,  Ijlb.,  l§lb.,  21b. 

3.  25  ct,  50  ct,  75  ct,  $1.25.  4.  $20,  $60,  $80. 

Page  159 

1.  226 J.         2.  449f.         3.  279 J.     4.  90|.  5.  249J. 

6.  134J.         7.  345i.         8.  4381.     9.  44  sq.  in. 

Page  160 

1.  640.  2.  666.  3.  243.  4.  423.  5.  540. 

6.  687.  7.  609.  8.  296.  9.  338.  10.  470. 

11.  534.  12.  582.  13.  616.  14.  489.  15.  391. 

16.  105.  17.  4971.  18.  65^.  19.  355J.  20.  85J. 


14  ANSWERS 

21.  3411.     22.  77§.  23.  95].      24.  92.  25.  797$. 

26.  89.         27.  25J.  28.  166£.    29.  199J.         30.  123. 

31.  115£.     32.  223.  33.  207$.    34.  96  cu.  in.  35.  170. 

36.  297.       37.  384.  38.  216.      39.  384.  40.  385. 

41.  208.       42.  4131  43.  126f.    44.  204*.         45.  140§. 

46.  39.         47.  39.  48.  39.        49.  49.  50.  71. 

51.  41.         52.  32.  53.  57.        54.  29.  55.  72. 

Page  161 

1.  3600  sq.  in.    2.  333  sq.  ft.    3.  16,  16,  16  sq.  yd. 

4.  240  sq.  yd.    5.  1664  sq.  ft.,  3654  sq.  yd.,  1936  sq.  ft. 


1. 

$165.75. 

Page  162 

2.  $187. 

3.  $6 

.10. 

Page  163 

1. 

4000  lb.,  6000  Ib. 

2. 

171  sq.  ft. 

3. 

2448  sq 

.  ft. 

4. 

192  sq.  yd. 

5. 

81  sq.  yd. 

6. 

108  sq. 

yd. 

7. 

432  sq.  yd. 

8. 

171  sq.  yd. 

9. 

576  sq. 

yd. 

10. 

174  sq.  yd. 

11. 

1452  sq.  yd. 

12. 

11,136. 

13. 

7527. 

14. 

10,397. 

15. 

9536. 

16. 

9207. 

17. 

5797. 

18. 

8892. 

19. 

8175. 

20. 

9174. 

21. 

8778. 

22. 

8928. 

23. 

7123. 

24. 

8832. 

25. 

10,449. 

26. 

9751. 

27. 

$46.99. 

28. 

$62.51. 

29. 

$74.24. 

30. 

$69.12. 

31. 

571. 

32. 

491. 

33. 

541. 

34. 

693. 

35. 

254f. 

36. 

670i. 

37. 

$2.55. 

38. 

$5.44^. 

39. 

$2.75f 

40. 

$2.54^. 

41. 

25. 

42. 

181. 

43. 

89. 

44. 

19. 

45. 

75. 

46. 

68. 

Page  164 
1.  28,  216,  2.    2.  8,  6,  4.     3.  $26.      4.  $11. 


ANSWERS  15 

Page  165 
1.  66  ft.  2.  300  ft.         3.  390  lb.,  6.     4.  54,000  gal. 

Page  166 

1.  9,  27.  2.  30. 

3.  16  oz.,  32  oz.,  4  oz.  4.  4  tumblers,  2  gills. 

Page  167 
3.  180  da. 

Page  169 

1.  10.  2.  36,550.  3.  731,  16.  4.  $160. 

Page  170 

1.  6946.            2.  7211.  3.  $192.98.           4.  $187.78. 

5.  $202.95.      6.  $772.68.  7.  $225.52.           8.  19,318. 

9.  38,418.       10.  20,584.  11.  144.                 12.  26. 

13.  125.            14.  41.  15.  33|.                 16.  71J. 

17.  43f            18.  231.  19.  26|.                 20.  19^. 

21.  24J.  22.  360,  240,  480,  180,  540. 

23.  288,  576,  864,  1152,  240,  1200. 

24.  110,  148,  314,  348.  25.  220,  272,  628,  3680. 
26.  480,  570,  84,  2430.  27.  252,  405,  495,  2583. 

Page  172 
1.  40,404,  70,747,  64,788,  98,765,  50,005,  66,666,  10,010. 

Page  173 

1.  $7456.         2.  $13,846.        3.  $32,320.        4.  $30,419. 
5.  $236.  6.  $129.  7.  $108.  8.  $88. 

9.  $309.         10.  $209. 

Page  175 

1.  $956.40.       2.  $713.75.       3.  $1626.97.     4.  $875.68. 
5.  $1015.34.     6.  $635.01.       7.  $907.64.       8.  $1247.0& 


16 


ANSWERS 


9.  $823.68.  10.  $1078.58.  11.  $812.97.  12.  $1123.63. 
13.  $1042.27.  14.  $1208.99.  15.  $2493.80.  16.  $1290.95. 
17.  $1147.15.  18.  $857.98.  19.  $722.18.  20.  $953.87. 


Page  177 

1. 

$146.40 

2. 

$483.73.       3.  $190.70. 

4.  $317.88. 

5. 

$294.98. 

6. 

$326.26.       7.  $89.32. 

8.  $123.14. 

9. 

$523.96. 

10. 

$221.88.     11.  $299.83. 

12.  $168.99. 

13. 

$92.84. 

14 

$185.36.     15.  $99.13. 

16.  $98.92. 

17. 

$86.89. 

18. 

^551.25.     19.  $444.22. 

20.  $530.19. 

21. 

$360.25. 

22. 

$148.60.     23.  $271.31. 

24.  $321.91. 

25. 

$550.11. 

26. 

$251.          27.  $341.85. 

28.  $587.31. 

29. 

$381.22. 

30. 

$261.44.     31.  $77.60. 

32.  $193.33. 

33. 

$537.35. 

34. 

$390.88.     35.  $877.55. 

Page  178 

1. 

8635. 

2. 

235.                 3.  530  ft. 

4.  173. 

5. 

189. 

6. 

$3540.45.       7.  $3277.25. 

Page  179 

1. 

76  ct.         2.  24  ct.,  96  ct.         3,  16  ct.,  80  ct. 

4. 

$3.25.        5.  $24. 

Page  180 

1. 

$1467.50. 

2.  $3378.20.               3 

.  $589050. 

4. 

$2973.76. 

5.  $2787.48.               6 

.   $4824.36. 

7. 

$6882.92. 

8.  $10,780.90.            9 

.  $8628.75. 

10. 

$10,974.96 

11.  $12,018.30.          12 

.  $24,668.75. 

13. 

$9689.90. 

14.  $17,021.44.          15 

.  $23,919. 

16. 

$23,949. 

17.  $35,432.80.          18 

.  $28,703.69. 

19. 

$36,147.06 

20.  $22,528. 

ANSWERS  17 


Page  181 

1. 

$59,500. 

2 

.  $99,387 

3 

.  $76,109. 

4. 

$229,402. 

5 

.  $3332.8 

8. 

6 

.  98,868. 

7. 

80,934. 

8 

.  $1843.75. 

9 

.  $33,747.20 

10. 

$28,988.40 

11 

.  $18,047 

.25. 

12 

.  $32,322.36. 

13. 

$42,093.44 

14 

.  $22,310 

.64. 

15 

.  $30,796.80. 

16. 

$34,689.75 

17 

.  $49,060 

.08. 

18 

.  $2543.32. 

19. 

$7976.50. 

20 

.  $39,832 

.56. 

21 

.  $13,940. 

22. 

$1425. 

23 

.  $42. 

24 

.  $101.25. 

25. 

$46.08. 

26 

.  $546. 

Page  182 

1. 

29.            2. 

139. 

3.  222. 

4. 

111 

5.  99. 

6. 

222.          7. 

$45. 

8.  $21. 

9. 

35. 

10.  $11. 

Page  183 

1 

$3.24.     2. 

dJ»Q    q  J^ 

3.  $2.17. 

4.   $1 

11 

5    $27.63- 

6. 

$3.64.     7. 

$1.35. 

8.  $7.20. 

9.  72 

ct. 

10.  38  ct. 

Page  184 

1. 

7*. 

2.  5f, 

3. 

m- 

4.  8J. 

5. 

1$. 

6.  10J. 

7. 

12i. 

8.  15. 

9. 

451. 

10.  67i. 

11. 

93f. 

12.  89^. 

13. 

65T8T. 

14.  39, 

15. 

81TV 

16,  67yV. 

17. 

$2.101 

18.  $3 

5£ 

;i.     19. 

$4.84i 

20.  $3.30^. 

Page  185 

1.  101.         2.  102.         3.  203.         4.  203.         5.  105. 

6.  901.         7.  40|f       8.  106if     9.  909i°.  10.  90££. 
11.  102.       12.  901i|.  13.  31  ct.     Fractions,  as  in  Ex.  7, 
may  be  replaced  by  remainders,  as  40  and  a  remainder  of  24. 


18 


ANSWERS 


Page  186 

1. 

202TV 

2.  146ft. 

3.  102. 

4. 

206TV 

5.  6071$. 

6.  147. 

7. 

$3.50,  $28. 

8.  $15.50. 

9.  $22.50. 

Page  187 

1. 

86.                 2. 

$117$.            3.  1047. 

4.  1040. 

5. 

1162.            6. 

427.                 7.  4504$. 

8.  1560$. 

9. 

1430.           10. 

10,487.         11.  3109. 

12.  6706. 

13. 

$12.06J.     14. 

$14.81$.      15.  $8.93-i. 

16.  $43.52J. 

17. 

$80.40$.     18. 

$27.77J. 

Page  188 

1. 

16,  495  rem. 

2.  83  ct.              3. 

$36,  $900  rem. 

4. 

$0.49. 

5.  81  ct.              6. 

$3.21. 

7. 

75  ct. 

8.  95.                   9. 

$7.25. 

10. 

$7.35. 

11.  50,  85  ct.      12. 

$103.39. 

13. 

$6.75. 

Page  189 

1. 

$8.75.              2 

.  $5.62.             3.  $99. 

4.  64  ct. 

5. 

16^V  ct.           6 

.  $2.78.             7.  87  ct. 

8.  $1.05. 

9. 

61  ct.              10 

.  89  ct.            11.  $2.10, 

12.  $6.25. 

13. 

$35.27.          14 

.  $10.50.         15.  65  ct. 

16.  35  ct. 

17. 

$25.44. 

Page  190 

1. 

97.                    2 

.  360.                  3.  859. 

4.  2254. 

5. 

$86.54.             6 

.  $220.               7.  88  ct. 

Page  191 
1.  $93.      2.  $348.      3.  $5.80.      4.  $244.20.      5.  $2.22. 


ANSWERS  19 

Page  192 

1.  19.        2.  3.          3.  29.  4.  20.  5.  32. 

8.  60.        7.  75.        8.  20,  28,  44,  48. 

9.  24,  30,  45,  60.    10.  27  ct. 

Page  194 

1.  62$.  2.  12J.         3.  12$.          4.  55J.  5.  12$. 

6.  35J.  7.  44-|.         8<  e§.  9.  12|.          10.  47£, 

11.  17$.         12.  18$. 


5.  15,  20,  5,  25. 


4.  12,299. 

8.  14,826$. 
12.  3404f. 
16.  3396f. 


5.  54. 

10.  55. 

15.  87. 

20.  126. 


Page  199 

1.  329.  2.  572.  3.  1058.  4.  9.86. 

5.  6767.  6.  5041.  7.  $275.  8.  $990. 

9.  $630.  10.  $17.60.  11.  $47.15.  12.  $43.86. 

13.  $343.75.  14.  $884.  15.  $1034.  16.  $242.50. 

17.  $660.38.  18.  $1385.10.  19.  $876.73.  20.  $653.33. 

21.  $16.20.  22.  $23.60.  23.  $55.20. 


3. 
6. 

6,  9,  3, 
12,  24, 

Page  196 

15.      4.  8,  16,  4,  20.     5. 
6,  30.     7.  21,  14,  7,  6. 

Page  197 

1. 

331|. 

2.  1000J. 

3. 

995§. 

5. 
9. 
13. 

1464^. 
4400|. 
7845J. 

6.  2018$. 
10.  1869f. 
14.  33371. 

7. 
11. 
15. 

1268J. 
7597$. 
12731. 

Page  198 

1. 

42. 

2.  50.     3. 

64. 

4.  51. 

6. 

72. 

7.  30.     8. 

45. 

9.  60. 

11. 

60. 

12.  80.     13. 

63. 

14.  69. 

16. 

215. 

17.  265.    18. 

355. 

19.  35. 

21. 

126. 

20 


ANSWERS 


Page  200 

1. 

$5.25. 

2.  $2.60, 

3.  91  ct. 

4. 

$13.76. 

5.  $4.08. 

6.  $7.49. 

Page  201 

1. 

39,483. 

2.  76,648. 

3. 

90,750. 

4. 

92,352. 

5.  74,556. 

6. 

78,141. 

7. 

57,057. 

8.  83,640. 

9. 

63,342. 

10. 

83,809. 

11.  62,624. 

12. 

41,808. 

13. 

54,400. 

14.  68,888. 

15. 

92,040. 

16. 

42,000.- 

17.  .$1891.98. 

18. 

$2290.08. 

19. 

$5129.25. 

20.  $2882.82. 

21. 

$11,813.75. 

22. 

$22,598.40 

23.  $23,796.48. 

24. 

$40,286.6C 

25. 

162. 

26.  42. 

27. 

48. 

28. 

87§§., 

29.  69jf. 

30. 

37|g-. 

31. 

12851. 

32.  82JJ. 

33. 

206ii. 

34. 

271. 

35.  242. 

36. 

203. 

37. 

302^. 

38.  325J. 

39. 

235i. 

40. 

107T55°^. 

41.  HlT4oV 

42. 

3717. 

43. 

5450.° 

44.  4995. 

45. 

8211. 

46. 

5136. 

47.  21,115. 

48. 

37,054. 

49. 

43,332. 

50.  67,039. 

51. 

3694J. 

Page  202 

1. 

5749.      2. 

2632.      3.  10. 

4.  9. 

5. 

2397  1.     6. 

4278|.     7.  2775-J. 

8.  6753^. 

9. 

791.      10. 

5600.     11.  5726*. 

12.  6385^. 

13. 

1404^.    14. 

2044.     15.  541  f\. 

16.  247, 

17. 

150.      18. 

332.      19.  176. 

20.  125. 

21. 

22327.     22. 

217Hf   23.  359^? 

. 

24.  124. 

25. 

242§.     26. 

193irgi.   27.  169^. 

28.  47212J. 

29. 

144^.   30. 

204f  j.    31.  72. 

32.  I42ijf 

33. 

395.      34. 

102. 

ANSWERS  21 

Page  203 

1.  42  pt.  2.  8  gal.  3.  88  pk.  4.  288  hr. 

5.  2350  ct.         6.  1500  sec.       7.  28  oz.  8.  9  min. 

Page  204 

1.  16i  ft.,  1  rd.         2.  2640  ft.,  1320  ft.,  660  ft. 
3.  160  rd.,  80  rd.,  40  rd.   4.  36  in.,  198  in.,  63,360  in.  j 
5.  2  mi.,  17  mi.         6.  264  yd.,  355  yd. 

Page  205 

1.  98  ft.,  558  sq.  ft.      2.  174  ft.,  1850  sq.  ft. 

3.  38|  ft.,  65  sq.  ft.      4.  540  sq.  in. 
5.  423  sq.  yd.  6;  372  sq.  ft. 

Page  206 

2.  60  sq.  in.,  30  sq.  in.    4.  49^  sq.  in. 

Page  207 

1.  3cu.ft.  2.  128  cu.  in.  3.  1105cu.in.  4.  168cu.  yd. 

Page  209 
1.  3025  sq.ft.          2.  185  J  yd. 

3.  29,700  sq.  ft.         4.  1,633,500  cu.  ft. 
5.  44,921,250  cu.  ft.      6.  7,636,612,500  Ib. 

Page  210 

1.  47  ft.  8  in.     2.  54  yd.  2  in.     3.  83  gal.  1  qt. 

4.  228  ft.  6  in.    5.  288  yd.        6.  231  bu.  1  pk. 
7.  189  Ib.  9  oz.    8.  285  yd.  31  in.    9.  199  Ib.  7  oz. 

Page  211 

1.  13  ft.  8  in.     2.  3  yd.  23  in.     3.  Ill  ft.  10  in. 

4.  105  gal.  3  qt.    5.  6  mi.  4380  ft.    6.  1  mi.,  5J  mi. 
7.  6|  mi. 


22  ANSWERS 

Page  212 

1.  900  sq.  in.  4.  2736  sq.  in.  5.  4558  sq.  in. 

6.  1536  sq.  mi.         7.  23,864  sq.  ft.         8.  62,568  sq.  yd. 
9.  6192  sq.  yd. 

Page  214 

10.  6,000,275.  11.  20,020,  2,000,202,  300,333. 

12.  5280,  52,800,  528,000,  1,056,000. 

13.  60,  3600,  86,400,  31,536,000,  315,360,000. 


Page  215 

1. 

$453.40. 

2.  557  Ib.  3  oz. 

3.  586  ft.  4  in. 

Page  216 

1. 

4. 

11  Ib.  8  oz. 
li  qt.,  10  ct. 

2.  6  ct. 
5.  40  ct. 

3.  |  Ib.,  6  ct. 

Page  217 

1. 

4. 
7. 

3  ft.  11  in. 
3  bu.  3  pk. 
113  Ib.  6  oz. 

2.  1  Ib.  14  oz. 
5.  $287.88. 
8.  107  Ib.  12  oz. 

3.  3  gal.  3  qt. 
6.  $614.85. 

Page  218 

1.  $85,260.    2.  $238,924.    3.  $450,452.    4.  $1,087,750. 
5.  $324.         6.  $999.96.      7.  $56.33,  $675.96. 

Page  219 

1.  $720,790.  2.  $1,219,624.             3.  $8937.50. 

4.  $8864.25.  5.  $12,900.80.             6.  $22,120. 

7.  $62,723.25.  8.  $122,173.92.  9.  $5200. 

10.  $5200.  11.  $5200.  12.  $5200. 

13.  $12,040.  14.  $16,666.25.  15,  $343,203.12. 


ANSWERS  23 

Page  220 

1.  $2500.  2.  $4950.  3.  $33,775. 

4.  $31,250.  5.  $29,400.  6.  $46,415. 

7.  $114,300.  8.  $493,980.               9.  $196,206. 

10.  $3,195,135.  11.  $2,282,175.  12.  $1,268,547. 

Page  221 
1.  90  ct.  2.  $4.10. 

Page  222 

3.   $3. 


A, 


Page  223 

>  W-     2-  A> 
A,  J>  i,  *>  i- 


Pagi 

e  224 

1        552 

2.   6| 

)3 

3 

jg.37 

4.   8«4. 

5.    l%7.      6.   3fjc 

7.   «yi. 

*         ! 
8.     3| 

J     * 
[-• 

9. 

*ji. 

10.     1J6. 

H.   401.   12.  i|ii. 

13       9  8  9_ 

,    14.  ±< 

F- 

15. 

^f^. 

16.  -V/- 

Page  225 

1.  12.       2.  32.       3.  37.       4.  15.  5.  12.       6.  12. 

7.  11*.     8.  81.        9.  9i.     10.  561.  11.  12J.   12.  18TV 

13.  16.     14.  12f.   15.  8t\.   16.  lOii.  17.  6^.   18.  4jf. 


Page  226 
1.  1230.  3.  560.  5.  48.  7.  12. 

Page  227 

1.  15,665.     2.  9675.      3.  183,850.    4.  1414.       5.  336. 
6.  1248.        7.  $7.35.     8.  $36.75.      9.  $86.      10.  $284. 


24  ANSWERS 

Page  228 

1.  «.  2.  1ft.  3.  ft.  4.   7i. 

5.  8ft.  6.  7|.  7.  7ft.  8.  5ft. 


9.  14 J.  10.  $20i.  11.  111TV 

Page  229 

1.  18J.  2.  553ft.  3.  766}.  4.  22i. 

5.  12f,  6.  1|.  7.  199}.  8.  190JJ. 

9.  26T\  10.  $12.25.  11. 


Page  231 
4.  J,  5.  J.  6.    i.  7.  i.  8.  f.  9.  f 

Page  234 
1.  $170.      2.  $177.60.      3.  $375.      4.  $128.      5.  $165. 

Page  235 
1.  87  Jet.  2.  $1.05.  3.  95  ct.  4.  $1.20. 


Page  236 

1. 

9T2- 

2. 

16f. 

3. 

T7T* 

4. 

$9J. 

5. 

$13ft. 

6. 

*fl\  1  *?  1 

7. 

45TV 

8. 

12T72. 

9. 

25ft. 

10. 

8fV 

11. 

18i. 

12. 

26|. 

13. 

3£  in. 

14. 

O  -I   .Cj. 

«-  (.  11. 

15. 

3f  in. 

16. 

41  f  Ib. 

17. 

5TT^  doz. 

18. 

50  ct. 

19. 

75  ct. 

20. 

$6. 

21. 

12,  36. 

22. 

12,  48. 

23. 

7,  35. 

24. 

6,  12. 

25. 

8,24. 

26. 

3,  15. 

27. 

30  in.,  40  in. 

28. 

$14,  $18. 

29. 

45  yd.,  60  rd. 

30. 

21  ft.,  45  in. 

31. 

105  ft. 

32. 

10£  qt. 

33. 

68  yd. 

ANSWERS  25 

Pages  238,  239 

1.  95  ct.       2.  $2.47.       3.  $3.      4.  $18.30.  5.  $5.87. 

Page  240 

1.  $1.25.  2.  58/.  3.  84/.  4.  48/. 

5.  88/.  6.  $1.08.  7.  22/.  8.  20/. 


9. 

75/. 

10. 

36/. 

11. 

24/. 

12. 

55/. 

13. 

30/. 

14. 

$3. 

15. 

35/. 

16. 

55/. 

17. 

$1.72. 

18. 

21/. 

19. 

63/. 

20. 

$1.34. 

21. 

76/. 

22. 

60/. 

23. 

$1.50. 

24. 

$1.60. 

25. 

56/. 

26. 

63/. 

27. 

33/. 

28. 

$1.20. 

29. 

$2.10. 

30. 

25X. 

31. 

49/. 

32. 

3l£/. 

33. 

.$1.02. 

34. 

$1.75. 

35. 

24^. 

36. 

88/. 

37. 

57i/. 

38. 

36/. 

Page  241 
1.  $3.?7.  2.  21  ct. 

Page  244 

1.  0.3,  0.5,  0.2,  0.6.  2.  0.03,  0.05,  0.07,  0.23. 

3.  0.47,  0.62,  0.54,  0.75.        4.  0.245,  0.625,  0.482,  0.003. 

5.  1.6,  3.5,  7.2,  9.6.  6.  1.32,  4.752,  $6.75. 

Page  245 

1.  ^,  0.2 ;  T^,  0.5.  2.  0.7,  0.6,  0.8,  0.9,  0.1. 

3-  TV>  t,  i,  i,  i,  I- 

Page  246 

1.  13.05.      2.  23.95.      3.  94.72.         4.  19.04.     5.  13.20. 

6.  22.30.      7.  221.15.    8.  355.325.     9.  9  ft. 

Page  247 

1.  $80.     2.  $225.         3.  $43.75.  4.  $62.50.  5.  $127.50. 
6.  $210.  7.  100  boys.  8.  21  lost.  9.  3. 


26  ANSWERS 

Page  248 
5.  $75.60.  6.  $6.40. 

Page  249 
1.  2800  sq.  rd.  2.  27,520  A.,  64,000  A.  3.  3  A. 

Page  250 

1.  5,000,000,000  lb.   2.  $500,000,000. 

3.  3,500,000  bales.     4.  2,000,000  bales,  1,000,000,000  Ib. 

Page  251 

2.  I  bu.  3.  £\  bu.  4.  1J  bu. 

Page  252 

1.  5  A.  2.  $1875. 

3.  10.  4.  264  ft.,  82  i  ft.,  21,780  sq.Tt.,  J  A. 
5.  $1375.  6.  $166.50. 

7.  $4500,  including  furniture.       8.  6  yr.  9.  $39.60. 

Page  253 

1.  22^  yd.  2.  $2.70.  3.  $1.75,  $2.05. 

4.  25  ct.  5.  $3.10.  6.  $1.50. 
7.  73£  ct.                     8.  $10.33J,  or  $10.34. 

Page  254 

4.  20  yd.  matting,  $9.60;  20  yd.  Brussels  carpet,  $13; 

26§  yd.  velvet  carpet,  $29.33 ;  but  it  would  really 
take  6  breadths  one  way  or  7  the  other,  costing 
$30.80  or  $33. 

Page  255 

1.  265,992.4  mi.  2.  1,589,160.  3.  1,628,640. 

4.  137.  5.  $1046.10. 


ANSWERS  27 

Page  256 
1.  1776  mi.     2.  $194.50.     3.  $30.     4.  485.5  T.,  5826  T. 

Page  257 


1. 

34.01. 

2.  150. 

3.  30.63. 

4. 

$5.82. 

5.  70.04. 

6.  10ft. 

7. 

10. 

8.  7  ft.  11  in. 

9.  17.32  in. 

10. 

310.1  ft. 

11.  65J  A. 

12.  122.82  in. 

13. 

$37.50. 

14.  $80. 

15.  $140. 

16. 

$123. 

17.  $309. 

18.  $370. 

19. 

$2262. 

20.  $110. 

21.  296  in. 

22. 

$475. 

23.  390  yd. 

24.  300  sq.  rd. 

25. 

375  cu.  in. 

26.  648  cu.  in. 

27.  59.18  sq.  ft. 

28. 

68.75  mi. 

29.  33.07  yd. 

30.  20.75  mi. 

31. 

1275.73  sq.  in. 

32.  9.37  in. 

33.  24yd. 

34. 

20.55  mi. 

35.  238.34  cu.  ft. 

36.  90/. 

37. 

$1.35. 

38.  $4.50. 

39.  $6.66f. 

40. 

45/. 

41.  $1.89. 

42.  84/. 

Page  258 

1. 

A,  0.05. 

2.  0.25,  25%. 

3.  1,  50%. 

Page  260 

1. 

$21.25.            2. 

$45.            3.  $7.50. 

4.  $32. 

5. 

$22.20.            6. 

$33.60.       7.  $27.50. 

8.  $66. 

9. 

$32.50.          10. 

$50.         11.  15. 

12.  5. 

13. 

110  girls.      14. 

1J  ft.        15.  7i  ft. 

16.  82,  41,  9. 

Page  261 

1. 

$62.50,  $187.50. 

2.  $48,  $272. 

3.  $55,  $385. 

4. 

$74.25,  $150.75. 

5.  $2.40,  $9.60. 

6.  $10,  $20. 

28  ANSWERS 

Page  262 

1.  $18.  2.  $40.  3.  $2.50.  4.  $45. 

s 

Page  263 


1. 

$40. 

2. 

$42. 

3. 

$30. 

4. 

$30. 

5. 

$4.50. 

6. 

$2.50. 

7. 

$1.50. 

8. 

$2. 

9. 

$6.25. 

10. 

$1.50. 

1 

1. 

$1.25. 

12. 

$8. 

Page  264 

1. 

831.4. 

2. 

6833. 

3 

.  3609.           4 

.'  4275. 

5. 

$4007.50.       6. 

$465.75. 

7 

.  78| 

ft. 

8 

.  535J  yd. 

9. 

32,736. 

10. 

2,021,250.   11 

.  241, 

500. 

12 

.  720. 

13. 

39,330. 

14. 

33,611. 

15 

.  $2628. 

16 

.  $962. 

17. 

17. 

18. 

$0.60. 

19 

.  23. 

20 

.  13. 

21. 

22.5. 

22. 

31.5. 

23 

.  $0.05. 

24 

.  $4.20. 

25. 

H  ft. 

26. 

111. 

27 

ill 

.12J. 

28 

.  101. 

29. 

101. 

30. 

3£  cu.  in. 

31 

•  i 

I- 

32 

•  ft- 

33. 

H- 

34. 

H- 

35 

•    TV 

36 

•  1- 

37. 

i- 

38. 

l« 

39 

•    I 

40 

•  t- 

41. 

0.6. 

42. 

0.8. 

43 

.  0.6. 

44 

.  0.9. 

45. 

0.33J. 

46. 

2.2. 

47 

.  3 

.4. 

48 

.  5.07. 

49. 

7.02. 

50. 

9.02. 

51. 

$38.40, 

$28,  $52,  $72,  $192, 

$412. 

52. 

$12,  $18.50. 

Page 

265 

1. 

<£>V 

2-  JJ- 

3. 

m- 

4 

.  ^. 

5. 

?v 

6. 

f. 

7.  f 

8. 

1- 

9 

•  f 

10. 

i- 

11. 

ftV 

12.  ^Vo 

13. 

i?i>- 

14 

•    TV 

15. 

i- 

16. 

7. 

i?-  m 

18. 

2.8.3  ^         I9e   -7,3-. 

20. 

IS  !_. 

21. 

23%. 

22.  42%. 

23. 

75% 

24 

.  62%. 

25. 

41%. 

26. 

20%. 

27.  30%. 

28. 

50%. 

29.  70%. 

30. 

80%. 

31. 

25%. 

32.  33^%. 

33. 

52%. 

34.  75%. 

35. 

82%. 

ANSWERS  29 

Page  266 

1.  1,  38,  55,  50,  4,  20,  30.          2.  10,  21,  26,  33,  3,  42,  53. 

3.  42,  10,  3,  4,  20,  56,  33.          4.  75,  1,  2,  16,  30,  34,  10. 

5.  45,  13,  31,  45,  14,  10,,20.     6.  11,  48,  56,  53,  4,  52,  63. 

7.  42,  21,  28,  34,  23,  66,  53.      8.  85,  11,  3,  19,  30,  66,  43. 

9.  77,  13,  33,  46,  34,  34,  20.  10.  43,  48,  58,  54,  24,  76,  63. 

11.  85,  22,  28,  49,  33,  76,  63.  12.  87,  23,  34,  49,  34,  66, 53. 

13.  86,  49,  58,  69,  34,  86,  73.  14.  87,  34,  59,  79,  37,  76,  73. 
15.  88,  61,  89,  99,  38,  86,  83. 

Page  267 

1.  11,  2,  10,  11,  30,  11,  2.          2.  2,  12,  11,  22,  1,  10,  11. 
3.  11,  11,  14,  2,  2,  2,  3.  4.  11,  21,  11,  11,  10,  2,  2. 

5.  3,  10,  20,  5,  1,  1,  2.  6.  20,  0,  10,  7,  3,  1,  2. 

7.  13,  14,  21,  33,  31,  21,  13.  8.  24,  25,  35,  35,  33,  23, 16. 

9.  35,  46,  46,  46,  43,  25,  18.  10.  38,  56,  66,  51,  44,  26,  20. 

11.  12,  3,  13,  13,  23,  30,  10.  12.  0,  8,  7,  10,  0,  10,  20. 

13.  20,  21,  32,  20,  20,  5,  2.  14.  12,  31,  10,  10,  9,  5,  1. 

15.  22,  3,  12,  12,  4,  4,  2.  16.  10,  1,  2,  3,  3,  4,  5. 

17.  12,  11,  20,  23,  23,  40,  30.  18.  32,  32,  52,  43,  43,  45, 32. 
19.  44,  63,  62,  53,  52,  50,  33. 

Page  269 

1.  68  ft.      2.  5,  10,  13.      4.  43.  5.  74  ml        6.  22. 

7.  30.          8.  23  ct.  9.  66  ct.      10.  48  ct.       11.  6. 

Page  271 

1.  $560.     2.680yd.     3.703ft.      4.  615  in.      5.  $730. 

6.  $702.     7.  800yd.     8.  766ft.       9.  888  in.    10.  $779. 
11.  916.      12.  912.         13.  983.         14.  737.         15.  885. 

16.  740.      17.  777.         18.  918.         19.  687.         20.  688. 
21.  $865.  22.  $744.      23.  $578.      24.  $852.      25.  $755. 


30  ANSWERS 

Page  272 


1. 

107. 

2. 

69. 

3. 

146. 

4. 

198. 

5. 

208. 

6. 

148. 

7. 

172. 

8. 

118. 

9. 

189. 

10. 

99. 

11. 

323. 

12. 

70. 

13. 

429. 

14. 

203. 

15. 

565. 

16. 

364. 

17. 

505. 

18. 

575. 

19. 

367. 

20. 

189. 

21. 

$148. 

22. 

$39. 

23. 

$174. 

24. 

$41. 

25. 

$91. 

26. 

$125. 

27. 

$365. 

28. 

$108. 

29. 

355  ft. 

30. 

94ft. 

31. 

114  yd. 

32. 

818  ft. 

33. 

99  bu. 

34. 

139  bu. 

35. 

85ft. 

36. 

248  bu. 

37. 

383  ft. 

38. 

284  ft. 

39. 

130  ft. 

40. 

171  ft. 

Page  273 

1.  64.        2.  87.       3.  188.       4.  265.  5.  260.      6.  305. 

7.  248.      8.  78.       9.  72.       10.  252.  11.  330.    12.  438. 

13.  135.    14.  252.   15.  162.     16.  90.  17.  172.    18.  195. 

Page  274 

1.  160.      2.  98.        3.  228.      4.  232.  5.  95.        6.  410. 

7.  108.      8.  165.      9.  94.      10.  258.  11.  145.    12.  192. 

13.  192.    14.  87.      15.  76.      16.  176.  17.  115.    18.  117. 

Page  275 

1.  112.      2.  111.      3.  312.      4.  111.  5.  123.      6.  211. 

7.  212.  8.  403.  9.  201.  10.  100.  11.  233.  12.  104. 

13.  102.  14.  210.  15.  412.  16.  222.  17.  23.  18.  110. 
19.  101.  20.  121.  21.  32. 

Pages  276,  277 

1.  255.          2.  337.         3.  264.         4.  257.            5.  366. 

6.  3149.       7.  3236.       8.  3704.       9.  4153.        10.  2503. 


ANSWERS 


31 


11. 

14. 
17. 
20. 

$475.19. 
$692.55. 
$1949.37. 
$1401.02. 

12.  $938.38.       13.  $952.49. 
15.  $581.53.       16.  $747.24. 
18,  $1912.99.       19.  $1190.72. 
21.  $1078.82.      22.  $4750.97. 

Page  278 

1. 

205f.      2. 

252f.      3.  9951 

4.  920J. 

5. 

16661,     6. 

3161.      7.  1642J. 

8.  701}. 

9. 

302f     10. 

448f.     11.  897f 

12.  355. 

13. 

507.      14. 

364J.     15.  398}. 

16.  904f. 

17. 

236f.     18. 

2931.     19.  908f. 

20.  1180a. 

21. 

1333J.    22. 

585}.     23.  888|. 

24.  667. 

25. 

440}.     26. 

1620.     27.  3888J. 

28.  1335f. 

29. 

18431.    30. 

1139J.    31.  1008|. 

32.  825}. 

Pages  279,  280 

1. 

72  ct.,  28  ct. 

2.  $1.04.         3. 

80  ct.,  20  ct. 

4. 

32  ct.,  18  ct. 

5.  69  ct.,  46  ct.    6. 

15  et. 

7. 

$1.45,  $3.55. 

8.  25  ct.         9. 

25  ct. 

10. 

35. 

11.  $15.         12. 

$224. 

13. 

$216. 

14.  264ft.       15. 

35. 

16. 

The  second,  $6. 

17.  126.         18. 

39. 

19. 

$32,  $192. 

20.  $46.45. 

Page  282 

1. 

$96. 

2.  $40.25. 

3.  1136  ft. 

4. 

175  bu. 

5.  $1822.80. 

6.  5. 

7. 

$302,250. 

8.  $3772. 

9.  1347. 

10. 

$17.45. 

Page  283 

1. 

$936. 

2.  1334  bu. 

3.  46  ct. 

4. 

$2.25. 

5.  $26.80. 

6.  $15. 

7. 

92. 

8.  $104.07. 

9.  8  hr. 

32  ANSWERS 


Page  284 

1.  1536  cu 

.  ft.                 2.  12  cd.                           3.  $90.75. 

4.  972. 

5.  216  sq.  ft.                    6.  $71.25. 

Page  285 

1.  $3,  $4. 

2.  $102,  $204.                3.  $600,  $480. 

4.  $10,  $9 

5.  8|.                                 6.  2ff. 

7.  |. 

8.  173||.                           9.  14TV 

Pages  286,  287 

1.  0.4,  or  .4.       2.  0.2,  or  .2.        3.  0.5,  or  .5.      4.  0.7,  or.  7. 

5.  0.3. 

6.  0.5.                 7.  0.7.                8.  0.25. 

9.  0.07. 

10.  2.5.               11.  3.75.             12.  3.7,  0.8. 

13.  42.42. 

14.  3.75,0.99.                     15.  300.75,0.05. 

16.  0.375. 

17.  4.5,7.5,0.85,0.55.        18.  300.075. 

19.  6.5,6.5, 

6.5,  6.5.                                    20.  0.515,  500.015. 

21.  7072  bu. 

22.  107.68ft.     23.  $1627.50.    24.  54.171b. 

25.  490.82  mi.  26.  15.                27.  33.3.             28.  33.6. 

29.  220. 

30.   196.2.           31.  216.              32.  5.29. 

33.  15.96. 

34.  21.06.           35.  96.48.           36.  208.98. 

37.  262.7. 

38.  136.8.           39.  193.44.         40.  251.79. 

41.  281.86. 

42.  468.66.         43.  269.41.         44.  $1.10. 

45.  87  ct. 

46.  90  ct.           47.  62  ct.           48.  60  ct. 

49.  $3.27. 

50.  81  ct.           51.   77  ct.           52.  28  ct. 

53.  $1.02. 

54-  i>  i>  i>  T£>  4V     55-  i>  i>  i?  iV  sV 

56.  J,  i,  TV 

J5,  ^i_.    57.  yi_?  ^  ^  ^i_.      58.  /o,  T\,  T^. 

59.  J,  ^,4, 

i,  £.                       '    60.  $690,  $1725,  $1581.25. 

61.  52ft.  9 

in.           62.  18  cd.                    63.  3300  sq.  in. 

Page  288 

1.  $408. 

2.  $717.             3.  $455.               4.  $192.50. 

5.  $164. 

6.  $143.64.        7.  $138.              8.  $246. 

9.  $19. 

10.  $29.             11.  70^ct,          12.  $1.32. 

13.  $12.26. 

14.  $5.20.                    or  71  ct.     15.  8125  Ib. 

THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  5O  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


SEP   131946 

LD  21-100m-12,'43(879 

10     I 


M3061.07 

Q 

5 


THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


